1) Initial set-up

Load packages for the analysis using the “pacman” package

if (!require("pacman")) install.packages("pacman")
## Loading required package: pacman
pacman::p_load(boot,MASS,readxl,plyr,ggplot2,lme4,lmerTest,lsmeans,gtsummary,ggthemes,patchwork,modelsummary,psych,
               lavaan,semTools,semPlot,expss)

Set the working directory (i.e., where the data are stored)

setwd("~/Desktop/OneDrive - UBC/UK Biobank Greenspace Analysis")

Load the data set * Notes: + 1) This dataset has been reduced from the full UKB dataset to the primary variables of interest for this analysis.

fulldata<-read.csv("UKB_Fulldata_Sept27_2023.csv") #Data#

2) Set-up variables for analysis

Change sex to male vs. female

fulldata$Sex[fulldata$Sex==1]<-"Male"
fulldata$Sex[fulldata$Sex==0]<-"Female"

Assessment centre

fulldata$Assessment_Centre<-NA
fulldata$Assessment_Centre[fulldata$Assessment.centre==11012]<-"Barts"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11021]<-"Birmingham"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11011]<-"Bristol"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11008]<-"Bury"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11003]<-"Cardiff"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11024]<-"Cheadle (revisit)"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11020]<-"Croydon"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11005]<-"Edinburgh"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11004]<-"Glasgow"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11018]<-"Hounslow"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11010]<-"Leeds"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11016]<-"Liverpool"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11001]<-"Manchester"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11017]<-"Middlesborough"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11009]<-"Newcastle"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11013]<-"Nottingham"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11002]<-"Oxford"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11007]<-"Reading"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11014]<-"Sheffield"
fulldata$Assessment_Centre[fulldata$Assessment.centre==10003]<-"Stockport (pilot)"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11006]<-"Stoke"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11022]<-"Swansea"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11023]<-"Wrexham"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11025]<-"Cheadle (imaging)"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11026]<-"Reading (imaging)"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11027]<-"Newcastle (imaging)"
fulldata$Assessment_Centre[fulldata$Assessment.centre==11028]<-"Bristol (imaging)"

Length of time at current address (3 timepoints [T0, T2, T3]) * Recorded in whole years. -10: less than a year; -1: do not know; -3: prefer not to answer

fulldata$Time_at_current_address_T0 <- fulldata$Length.of.time.at.current.address.0
fulldata$Time_at_current_address_T0[fulldata$Time_at_current_address_T0==-10] <- 0.5
fulldata$Time_at_current_address_T0[fulldata$Time_at_current_address_T0==-1 | fulldata$Time_at_current_address_T0==-3] <- NA

fulldata$Time_at_current_address_T2 <- fulldata$Length.of.time.at.current.address.2
fulldata$Time_at_current_address_T2[fulldata$Time_at_current_address_T2==-10] <- 0.5
fulldata$Time_at_current_address_T2[fulldata$Time_at_current_address_T2==-1 | fulldata$Time_at_current_address_T2==-3] <- NA

fulldata$Time_at_current_address_T3 <- fulldata$Length.of.time.at.current.address.3
fulldata$Time_at_current_address_T3[fulldata$Time_at_current_address_T3==-10] <- 0.5
fulldata$Time_at_current_address_T3[fulldata$Time_at_current_address_T3==-1 | fulldata$Time_at_current_address_T3==-3] <- NA

Household Income

fulldata$Income<-NA
fulldata$Income[fulldata$Household.Income==1]<- "<18,000 GBP"
fulldata$Income[fulldata$Household.Income==2]<- "18,000-30,999 GBP"
fulldata$Income[fulldata$Household.Income==3]<- "31,000-51,999 GBP"
fulldata$Income[fulldata$Household.Income==4]<- "52,000-100,000 GBP"
fulldata$Income[fulldata$Household.Income==5]<- ">100,000 GBP"
fulldata$Income[fulldata$Household.Income<=0]<- "Do not know or prefer not to answer"

Time spent outdoors (categorical variable)

#Time spent outdoors in summer (categorical)
fulldata$Time_outdoors_summer<-NA
fulldata$Time_outdoors_summer[fulldata$Time.spent.outdoors.in.summer==0 | fulldata$Time.spent.outdoors.in.summer==-10]<-"Less than 1 hour/day"
fulldata$Time_outdoors_summer[fulldata$Time.spent.outdoors.in.summer==-3 | fulldata$Time.spent.outdoors.in.summer==-1]<-"Do not know or prefer not to say"
fulldata$Time_outdoors_summer[fulldata$Time.spent.outdoors.in.summer>=1 & fulldata$Time.spent.outdoors.in.summer<7]<-"1-6 hours/day"
fulldata$Time_outdoors_summer[fulldata$Time.spent.outdoors.in.summer>=7 & fulldata$Time.spent.outdoors.in.summer<13]<-"7-12 hours/day"
fulldata$Time_outdoors_summer[fulldata$Time.spent.outdoors.in.summer>=13]<-"13+ hours/day"

#Time spent outdoors in winter (categorical)
fulldata$Time_outdoors_winter<-NA
fulldata$Time_outdoors_winter[fulldata$Time.spent.outdoors.in.winter==0 | fulldata$Time.spent.outdoors.in.winter==-10]<-"Less than 1 hour/day"
fulldata$Time_outdoors_winter[fulldata$Time.spent.outdoors.in.winter==-3 | fulldata$Time.spent.outdoors.in.winter==-1]<-"Do not know or prefer not to say"
fulldata$Time_outdoors_winter[fulldata$Time.spent.outdoors.in.winter>=1 & fulldata$Time.spent.outdoors.in.winter<7]<-"1-6 hours/day"
fulldata$Time_outdoors_winter[fulldata$Time.spent.outdoors.in.winter>=7 & fulldata$Time.spent.outdoors.in.winter<13]<-"7-12 hours/day"
fulldata$Time_outdoors_winter[fulldata$Time.spent.outdoors.in.winter>=13]<-"13+ hours/day"

Time spent outdoors (continuous variable)

#Time spent outdoors in summer (continuous)
fulldata$Time_outdoors_summer_cont<-fulldata$Time.spent.outdoors.in.summer
fulldata$Time_outdoors_summer_cont[fulldata$Time_outdoors_summer_cont==-10]<-0.5
fulldata$Time_outdoors_summer_cont[fulldata$Time_outdoors_summer_cont==-1 | fulldata$Time_outdoors_summer_cont==-3]<-NA

#Time spent outdoors in winter (continuous)
fulldata$Time_outdoors_winter_cont<-fulldata$Time.spent.outdoors.in.winter
fulldata$Time_outdoors_winter_cont[fulldata$Time_outdoors_winter_cont==-10]<-0.5
fulldata$Time_outdoors_winter_cont[fulldata$Time_outdoors_winter_cont==-1 | fulldata$Time_outdoors_winter_cont==-3]<-NA

#Time spent outdoors, averaged over summer and winter (continuous)
fulldata$Average_time_outdoors <- (fulldata$Time_outdoors_summer_cont + fulldata$Time_outdoors_winter_cont) / 2

Disability or infirmity status

fulldata$Disability<-NA
fulldata$Disability[fulldata$Disability.or.Infirmity.status==1]<-"Yes"
fulldata$Disability[fulldata$Disability.or.Infirmity.status==0]<-"No"
fulldata$Disability[fulldata$Disability.or.Infirmity.status<=-1]<-"Don't know or prefer not to answer"

Hearing difficulty status

fulldata$Hearing_difficulty<-NA
fulldata$Hearing_difficulty[fulldata$Hearing.Difficulty==99]<-"Completely Deaf"
fulldata$Hearing_difficulty[fulldata$Hearing.Difficulty==1]<-"Difficulty Hearing"
fulldata$Hearing_difficulty[fulldata$Hearing.Difficulty==0]<-"No Difficulty"
fulldata$Hearing_difficulty[fulldata$Hearing.Difficulty<=-1]<-"Don't know or prefer not to answer"

Diabetes status

fulldata$Diabetes<-NA
fulldata$Diabetes[fulldata$Diabetes.status==1]<-"Yes"
fulldata$Diabetes[fulldata$Diabetes.status==0]<-"No"
fulldata$Diabetes[fulldata$Diabetes.status<=-1]<-"Don't know or prefer not to answer"

Cancer status

fulldata$Cancer<-NA
fulldata$Cancer[fulldata$Cancer.status==1]<-"Yes"
fulldata$Cancer[fulldata$Cancer.status==0]<-"No"
fulldata$Cancer[fulldata$Cancer.status<=-1]<-"Don't know or prefer not to answer"

Other serious medical condition status

fulldata$Other_medical_conditions<-NA
fulldata$Other_medical_conditions[fulldata$Other.serious.medical.condition==1]<-"Yes"
fulldata$Other_medical_conditions[fulldata$Other.serious.medical.condition==0]<-"No"
fulldata$Other_medical_conditions[fulldata$Other.serious.medical.condition<=-1]<-"Don't know or prefer not to answer"

Educational attainment

fulldata$Education[fulldata$Education==1]<-"College or University Degree"
fulldata$Education[fulldata$Education==2]<-"A levels/AS levels or equivalent"
fulldata$Education[fulldata$Education==3]<-"O levels/General Certificate of Secondary Education or equivalent"
fulldata$Education[fulldata$Education==4]<-"CSEs or equivalent"
fulldata$Education[fulldata$Education==5]<-"National Vocational Qualification or equivalent"
fulldata$Education[fulldata$Education==6]<-"Other professional qualifications"
fulldata$Education[fulldata$Education==-7]<-"None of the above"
fulldata$Education[fulldata$Education==-3]<-"Prefer not to answer"

Employment status

fulldata$Employment[fulldata$Employment==1]<-"In paid employment or self-employed"
fulldata$Employment[fulldata$Employment==2]<-"Retired"
fulldata$Employment[fulldata$Employment==3]<-"Looking after home and/or family"
fulldata$Employment[fulldata$Employment==4]<-"Unable to work because of sickness or disability"
fulldata$Employment[fulldata$Employment==5]<-"Unemployed"
fulldata$Employment[fulldata$Employment==6]<-"Doing unpaid or voluntary work"
fulldata$Employment[fulldata$Employment==7]<-"Student"
fulldata$Employment[fulldata$Employment==-3]<-"Prefer not to answer"
fulldata$Employment[fulldata$Employment==-7]<-"None of the above"

Eye problems (data only available from ~30,000 participants)

fulldata$Eye_problems<-NA
fulldata$Eye_problems[fulldata$Eye.problems==1 | fulldata$Eye.problems==2 | fulldata$Eye.problems==3 | fulldata$Eye.problems==4 | fulldata$Eye.problems==5 | fulldata$Eye.problems==6]<-"Yes"
fulldata$Eye_problems[fulldata$Eye.problems==-7]<-"No"
fulldata$Eye_problems[fulldata$Eye.problems==-3]<-"Prefer not to answer"
fulldata$Eye_problems[fulldata$Eye.problems==-1]<-"Do not know"

Cardiovascular disease status

#Cardiovascular Disease
fulldata$CVD_problems<-NA
fulldata$CVD_problems[fulldata$CVD.problems==1 |fulldata$CVD.problems==2 | fulldata$CVD.problems==3 |
                     fulldata$CVD.problems==4]<-"Yes"
fulldata$CVD_problems[fulldata$CVD.problems==-7]<-"No"
fulldata$CVD_problems[fulldata$CVD.problems==-3]<-"Prefer not to answer"

Blood clots, allergies, and breathing problems status

fulldata$Clots_Asthma_Allergies<-NA
fulldata$Clots_Asthma_Allergies[fulldata$Blood.clots.and.breathing.problems==5 | fulldata$Blood.clots.and.breathing.problems==7 |
                               fulldata$Blood.clots.and.breathing.problems==6 |fulldata$Blood.clots.and.breathing.problems==8 |
                               fulldata$Blood.clots.and.breathing.problems==9]<-"Yes"
fulldata$Clots_Asthma_Allergies[fulldata$Blood.clots.and.breathing.problems==-7] <- "No"
fulldata$Clots_Asthma_Allergies[fulldata$Blood.clots.and.breathing.problems==-3] <- "Prefer not to answer"

Alcohol consumption

fulldata$Alcohol<-NA
fulldata$Alcohol[fulldata$Alcohol.intake==0]<-"Never"
fulldata$Alcohol[fulldata$Alcohol.intake==1]<-"Previous drinker"
fulldata$Alcohol[fulldata$Alcohol.intake==2]<-"Current drinker"
fulldata$Alcohol[fulldata$Alcohol.intake==-3]<-"Prefer not to answer"

Smoking status

fulldata$Smoking<-NA
fulldata$Smoking[fulldata$Smoking.Status==0]<-"Never"
fulldata$Smoking[fulldata$Smoking.Status==1]<-"Previous Smoker"
fulldata$Smoking[fulldata$Smoking.Status==2]<-"Current Smoker"
fulldata$Smoking[fulldata$Smoking.Status==-3]<-"Prefer not to answer"

Home area population density

fulldata$Population_density<-NA
fulldata$Population_density[fulldata$Home.area.population.density==1 | fulldata$Home.area.population.density==5 | 
                fulldata$Home.area.population.density==11 | fulldata$Home.area.population.density==12]<-"Urban area"
fulldata$Population_density[fulldata$Home.area.population.density==2 | fulldata$Home.area.population.density==6 | 
                           fulldata$Home.area.population.density==13]<-"Town"
fulldata$Population_density[fulldata$Home.area.population.density==3 | fulldata$Home.area.population.density==4 | 
                           fulldata$Home.area.population.density==7 | fulldata$Home.area.population.density==8 |
                           fulldata$Home.area.population.density>=14]<-"Village, Hamlet, or Rural Area"
fulldata$Population_density[fulldata$Home.area.population.density==9]<-"Postcode not linkable" 

Bipolar/Depression Status

fulldata$Bipolar_Depression<-NA
fulldata$Bipolar_Depression[fulldata$Bipolar.and.depression.status==0]<-"No Bipolar or Depression"
fulldata$Bipolar_Depression[fulldata$Bipolar.and.depression.status==1 | 
                           fulldata$Bipolar.and.depression.status==2]<-"Bipolar Disorder"
fulldata$Bipolar_Depression[fulldata$Bipolar.and.depression.status==3 | 
                           fulldata$Bipolar.and.depression.status==4]<-"Probable Recurrent Major Depressive Disorder"
fulldata$Bipolar_Depression[fulldata$Bipolar.and.depression.status==5]<-"Probable Single Major Depressive Episode"

Ethnicity/Race

fulldata$Race<-NA
fulldata$Race[fulldata$Ethnicity==1001 | fulldata$Ethnicity==1002 | fulldata$Ethnicity==1003]<-"White"
fulldata$Race[fulldata$Ethnicity==2001 | fulldata$Ethnicity==2002 | fulldata$Ethnicity==2003 | fulldata$Ethnicity==2004]<-"Mixed"
fulldata$Race[fulldata$Ethnicity==3001 | fulldata$Ethnicity==3002 | fulldata$Ethnicity==3003 | fulldata$Ethnicity==3004]<-"Asian or Asian British"
fulldata$Race[fulldata$Ethnicity==4001 | fulldata$Ethnicity==4002 | fulldata$Ethnicity==4003]<-"Black or Black British"

Age

fulldata$Age<-fulldata$Baseline.Age

Physical Activity Variables * Note: Summed_PA_min is PER DAY * Walking, Moderate PA, and Vigorous PA values are MET min/week. IPAQ conversion is: Walking = 3.3 METs, Moderate PA = 4.0 METs, and Vigorous PA = 8.0 METs

fulldata$Summed_PA_min<-fulldata$Summed.minutes.week.of.PA

fulldata$Summed_walking_min<-fulldata$MET.minutes.week.of.walking

fulldata$Summed_moderate_PA_min<-fulldata$MET.minutes.week.of.moderate.PA

fulldata$Summed_vigorous_PA_min<-fulldata$MET.minutes.week.of.vigorous.PA

fulldata$Summed_PA_MET_min<- (fulldata$Summed_walking_min + fulldata$Summed_moderate_PA_min + fulldata$Summed_vigorous_PA_min)

Index of Multiple Deprivation

fulldata$Deprivation_Index<-NA
fulldata$Deprivation_Index[!is.na(fulldata$Index.of.multiple.deprivation.England) &
                          is.na(fulldata$Index.of.multiple.deprivation.Scotland) &   is.na(fulldata$Index.of.multiple.deprivation.Wales)]<-fulldata$Index.of.multiple.deprivation.England
## Warning in
## fulldata$Deprivation_Index[!is.na(fulldata$Index.of.multiple.deprivation.England)
## & : number of items to replace is not a multiple of replacement length
fulldata$Deprivation_Index[is.na(fulldata$Index.of.multiple.deprivation.England) &
                          !is.na(fulldata$Index.of.multiple.deprivation.Scotland) &
is.na(fulldata$Index.of.multiple.deprivation.Wales)]<-fulldata$Index.of.multiple.deprivation.Scotland
## Warning in
## fulldata$Deprivation_Index[is.na(fulldata$Index.of.multiple.deprivation.England)
## & : number of items to replace is not a multiple of replacement length
fulldata$Deprivation_Index[is.na(fulldata$Index.of.multiple.deprivation.England) &
                          is.na(fulldata$Index.of.multiple.deprivation.Scotland) &
                          !is.na(fulldata$Index.of.multiple.deprivation.Wales)]<-fulldata$Index.of.multiple.deprivation.Wales
## Warning in
## fulldata$Deprivation_Index[is.na(fulldata$Index.of.multiple.deprivation.England)
## & : number of items to replace is not a multiple of replacement length

Neuropsychological testing variables * “DSST” actually refers to Symbol Digit (not Digit Symbol) Substitution test * For Pairs Matching, index 1 refers to the second round of the test, involving 6 pairs of cards.

#Pairs Matching Score - this code corrected Jan. 9, 2025
fulldata$Pairs_matching_correct<-NA
fulldata$Pairs_matching_correct[!is.na(fulldata$Pairs.Matching.Correct.1)]<-fulldata$Pairs.Matching.Correct.1
## Warning in
## fulldata$Pairs_matching_correct[!is.na(fulldata$Pairs.Matching.Correct.1)] <-
## fulldata$Pairs.Matching.Correct.1: number of items to replace is not a multiple
## of replacement length
fulldata$Pairs_matching_incorrect<-NA
fulldata$Pairs_matching_incorrect[!is.na(fulldata$Pairs.Matching.Incorrect.1)]<-fulldata$Pairs.Matching.Incorrect.1
## Warning in
## fulldata$Pairs_matching_incorrect[!is.na(fulldata$Pairs.Matching.Incorrect.1)]
## <- fulldata$Pairs.Matching.Incorrect.1: number of items to replace is not a
## multiple of replacement length
#Trails B-A
fulldata$Trails_B_A<- fulldata$Trails.B.Time - fulldata$Trails.A.Time


#Symbol Digit Substitution Score
fulldata$Symbol.Digit<-fulldata$DSST.Total.Score

#Fluid Intelligence Score
fulldata$Fluid_intelligence<-fulldata$Fluid.Intellgence.Score

#Numeric Memory Score
fulldata$Numeric_memory<-fulldata$Numeric.Memory.Score

Greenspace and environmental variables (T0)

#Greenspace percentage
fulldata$Greenspace_pcnt_1000m<-fulldata$Greenspace.percentage.1000m.0
fulldata$Greenspace_pcnt_300m<-fulldata$Greenspace.percentage.300m.0

#Natural Environment percentage
fulldata$Natural_environment_pcnt_1000m<-fulldata$Natural.environment.percentage.1000m.0
fulldata$Natural_environment_pcnt_300m<-fulldata$Natural.environment.percentage.300m.0

Brain volumes variables (2 timepoints [T2, T3]) * Using “Volumetric scaling from T1 image to standard space”, we calculated HPC volumes adjusted for head size.

#Grey matter volume (adjusted for head size)
fulldata$Grey_matter_volume_adjusted_T2<- fulldata$Grey.Matter.Volume..normalized.for.head.size..2
fulldata$Grey_matter_volume_adjusted_T3<- fulldata$Grey.Matter.Volume..normalized.for.head.size..3

#Grey matter volume (unadjusted)
fulldata$Grey_matter_volume_unadjusted_T2<- fulldata$Grey.Matter.Volume.unadjusted.2
fulldata$Grey_matter_volume_unadjusted_T3<- fulldata$Grey.Matter.Volume.unadjusted.3

#White matter volume (adjusted for head size)
fulldata$White_matter_volume_adjusted_T2<- fulldata$White.Matter.Volume..normalized.for.head.size..2
fulldata$White_matter_volume_adjusted_T3<- fulldata$White.Matter.Volume..normalized.for.head.size..3

#White matter volume (unadjusted)
fulldata$White_matter_volume_unadjusted_T2<- fulldata$White.Matter.Volume.unadjusted.2
fulldata$White_matter_volume_unadjusted_T3<- fulldata$White.Matter.Volume.unadjusted.3

#Total brain volume (adjusted for head size)
fulldata$Total_brain_volume_adjusted_T2 <- fulldata$Total.brain.volume..normalized.for.head.size..2
fulldata$Total_brain_volume_adjusted_T3 <- fulldata$Total.brain.volume..normalized.for.head.size..3

#Total brain volume (unadjusted)
fulldata$Total_brain_volume_adjusted_T2 <- fulldata$Total.brain.volume.unadjusted.2
fulldata$Total_brain_volume_adjusted_T3 <- fulldata$Total.brain.volume.unadjusted.3

#Hippocampal volume (Left Hemisphere; unadjusted)
fulldata$L_Hippocampal_volume_T2 <- fulldata$Left.hippocampal.volume.unadjusted.2
fulldata$L_Hippocampal_volume_T3 <- fulldata$Left.hippocampal.volume.unadjusted.2

#Hippocampal volume (Left Hemisphere; adjusted for head size)
fulldata$L_Hippocampal_volume_adjusted_T2 <- fulldata$L_Hippocampal_volume_T2 * fulldata$Volumetric.scaling.2
fulldata$L_Hippocampal_volume_adjusted_T3 <- fulldata$L_Hippocampal_volume_T3 * fulldata$Volumetric.scaling.3

#Hippocampal volume (Right Hemisphere; unadjusted)
fulldata$R_Hippocampal_volume_T2 <- fulldata$Right.hippocampal.volume.unadjusted.2
fulldata$R_Hippocampal_volume_T3 <- fulldata$Right.hippocampal.volume.unadjusted.3

#Hippocampal volume (Right Hemisphere; adjusted for head size)
fulldata$R_Hippocampal_volume_adjusted_T2 <- fulldata$R_Hippocampal_volume_T2 * fulldata$Volumetric.scaling.2
fulldata$R_Hippocampal_volume_adjusted_T3 <- fulldata$R_Hippocampal_volume_T3 * fulldata$Volumetric.scaling.3

#Average hippocampal volume (unadjusted)
fulldata$Avg_Hippocampal_volume_T2 <- (fulldata$L_Hippocampal_volume_T2 + fulldata$R_Hippocampal_volume_T2)/2
fulldata$Avg_Hippocampal_volume_T3 <- (fulldata$L_Hippocampal_volume_T3 + fulldata$R_Hippocampal_volume_T3)/2

#Average hippocampal volume (adjusted for head size)
fulldata$Avg_Hippocampal_volume_adjusted_T2 <- (fulldata$L_Hippocampal_volume_adjusted_T2 + fulldata$R_Hippocampal_volume_adjusted_T2)/2
fulldata$Avg_Hippocampal_volume_adjusted_T3 <- (fulldata$L_Hippocampal_volume_adjusted_T3 + fulldata$R_Hippocampal_volume_adjusted_T3)/2

#Total white matter hyperintensity volume
fulldata$Total_WMH_volume_T2<-fulldata$Total.volume.of.white.matter.hyperintensities.2
fulldata$Total_WMH_volume_T3<-fulldata$Total.volume.of.white.matter.hyperintensities.3

3) Determining final data set based on inclusion/exclusion criteria

First, only participants without stroke, Parkinson’s, or dementia are included (N=483,664)

included<-subset(fulldata, grepl("^\\s*$", Stroke.Date) & grepl("^\\s*$", Date.of.All.Cause.Dementia) & grepl("^\\s*$", Date.of.Parkinsons.Disease) &
                   CVD.problems!=3)
length(included$ID)
## [1] 483664

*Note: Counts for “included” and “excluded” do not sum to “fulldata” because missing (NA) values for CVD.problems will return false for both CVD.problems!=3 and CVD.problems==3. Therefore, adjust “included” to also include those with NA for CVD.problems.

included2<-subset(fulldata, grepl("^\\s*$", Stroke.Date) & grepl("^\\s*$", Date.of.All.Cause.Dementia) & grepl("^\\s*$", Date.of.Parkinsons.Disease) & (CVD.problems!=3 | is.na(CVD.problems)))
length(included2$ID)
## [1] 484559

Excluded participants (N=17,863)

Excluded<-subset(fulldata, !grepl("^\\s*$", Stroke.Date) | !grepl("^\\s*$", Date.of.All.Cause.Dementia) | !grepl("^\\s*$", Date.of.Parkinsons.Disease) |
                   CVD.problems==3)
length(Excluded$ID)
## [1] 17863

For the combined cognitive and brain analysis, only participants with complete cognitive and brain data were included (N= 17,494)

CogsBrain<- subset(included, !is.na(Grey_matter_volume_adjusted_T2) & !is.na(White_matter_volume_adjusted_T2) &
 !is.na(Avg_Hippocampal_volume_adjusted_T2) &
                  !is.na(Trails_B_A) & !is.na(Symbol.Digit) &
                 !is.na(Greenspace.percentage.1000m.0) & !is.na(Greenspace.percentage.300m.0) &
                  !is.na(Natural.environment.percentage.1000m.0) & !is.na(Natural.environment.percentage.300m.0))
length(CogsBrain$ID)
## [1] 17494

For the final analytical sample, only participants with complete cognitive, brain, and covariate data were included (N=11,448) * Observations were excluded if any values for the above were: NA, “Do not know or prefer not to answer”,“Do not know or prefer not to say”,“Don’t know or prefer not to answer”,“Prefer not to answer”, “Do not know”, “Postcode not linkable”.

#include observations if the values are not missing
CogsBrainCov <- included[!apply(included[c("Grey_matter_volume_adjusted_T2","White_matter_volume_adjusted_T2","Trails_B_A","Symbol.Digit","Greenspace.percentage.1000m.0","Greenspace.percentage.300m.0","Natural.environment.percentage.1000m.0","Natural.environment.percentage.300m.0","Age","Sex","BMI","Education","Income","Average_time_outdoors","Summed_PA_min","Smoking","Disability","Deprivation_Index","Population_density")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(CogsBrainCov$ID)
## [1] 11448

*Adjusted final analytical sample, starting from “included2”. Luckily, this leads to the same final sample as that derived from “included”, so no further adjustments need to be made.

#include observations if the values are not missing
CogsBrainCov2 <- included2[!apply(included2[c("Grey_matter_volume_adjusted_T2","White_matter_volume_adjusted_T2","Trails_B_A","Symbol.Digit","Greenspace.percentage.1000m.0","Greenspace.percentage.300m.0","Natural.environment.percentage.1000m.0","Natural.environment.percentage.300m.0","Age","Sex","BMI","Education","Income","Average_time_outdoors","Summed_PA_min","Smoking","Disability","Deprivation_Index","Population_density")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(CogsBrainCov2$ID)
## [1] 11448

Check distribution of missing data across nature exposure, brain structure, cognitive functions, and covariates

#missing nature exposure
missingNature <- included2[apply(included2[c("Greenspace.percentage.1000m.0","Greenspace.percentage.300m.0","Natural.environment.percentage.1000m.0","Natural.environment.percentage.300m.0")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(missingNature$ID)
## [1] 59343
#missing brain structure
missingBrain <- included2[apply(included2[c("Grey_matter_volume_adjusted_T2","White_matter_volume_adjusted_T2")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(missingBrain$ID)
## [1] 442279
#missing cognitive function
missingCog <- included2[apply(included2[c("Trails_B_A","Symbol.Digit")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(missingCog$ID)
## [1] 384875
#missing covariates
missingCovars <- included2[apply(included2[c("Age","Sex","BMI","Education","Income","Average_time_outdoors","Summed_PA_min","Smoking","Disability","Deprivation_Index","Population_density")], 1, function(row) any(row %in% c("Do not know or prefer not to answer","Do not know or prefer not to say","Don't know or prefer not to answer","Prefer not to answer", "Do not know", "Postcode not linkable") | is.na(row))), ]
length(missingCovars$ID)
## [1] 243648

These are the simplified data sets we’ll be using for 1) the full data set (i.e., all ~500,000 participants), 2) participants with both cognitive and brain data (N= 17,494), and 3) participants with cognitive, brain, and covariate data (N= 11,448).

Full.df<-fulldata[c(1,113,4,11,112,94,5,6,108,109,106,107,102,103,101,105,100,111,104,114,115,118,97:99,119,110,122,123,126:129,130,131,134,135,138,139,150:153,91:93,41,43,44)]

CogsBrain.df<-CogsBrain[c(1,113,4,11,112,94,5,6,108,109,106,107,102,103,101,105,100,111,104,114,115,118,97:99,119,110,122,123,126:129,130,131,134,135,138,139,150:153,91:93,41,43,44)]

CogsBrainCov.df<-CogsBrainCov[c(1,113,4,11,112,94,5,6,108,109,106,107,102,103,101,105,100,111,104,114,115,118,97:99,119,110,122,123,126:129,130,131,134,135,138,139,150:153,91:93,41,43,44)]

#Adding the other 3 cognitive function tests
CogsPlusBrainCov.df <- CogsBrainCov[c(1,113,4,11,112,94,5,6,108,109,106,107,102,103,101,105,100,111,104,114,115,118,97:99,119,110,122,123,124,125,121,126:129,130,131,134,135,138,139,150:153,91:93,41,43,44)]

This step creates variable labels that are easy to understand in the data output.

Full.df = apply_labels(Full.df,
                       Age = "Age (years)",
                       BMI = "Body Mass Index (kg/m^2)",
                       Income = "Household Income",
                       Time_outdoors_summer_cont = "Time outdoors in the summer (hours/day)",
                       Time_outdoors_winter_cont = "Time outdoors in the winter (hours/day)",
                       Average_time_outdoors = "Average time outdoors (hours/day)",
                       Hearing_difficulty = "Hearing problems",
                       Eye_problems = "Eye problems",
                       Disability = "Living with a disability or long-term illness",
                       Diabetes = "Living with diabetes mellitus",
                       Cancer = "Living with or previously had cancer",
                       Other_medical_conditions = "Living with another serious medical condition",
                       CVD_problems = "Living with cardiovascular disease",
                       Clots_Asthma_Allergies = "Living with blood clots, allergies, or asthma",
                       Bipolar_Depression = "Living with Bipolar Disorder or Depression",
                       Alcohol = "Alcohol drinking status",
                       Smoking = "Smoking status",
                       Population_density = "Home area population density",
                       Summed_PA_min = "Total physical activity (min/day)",
                       Summed_walking_min = "Total walking (MET min/week)",
                       Summed_PA_MET_min = "Total physical activity (MET min/week)",
                       Trails_B_A = "Trail making test (B-A; sec)",
                       Symbol.Digit = "Symbol digit substitution test (correct matches)",
                       Greenspace_pcnt_300m = "Greenspace percentage (buffered to 300 meters)",
                       Greenspace_pcnt_1000m = "Greenspace percentage (buffered to 1000 meters)",
                       Natural_environment_pcnt_300m = "Natural environment percentage (buffered to 300 meters)",
                       Natural_environment_pcnt_1000m = "Natural environment percentage (buffered to 1000 meters)",
                       Deprivation_Index = "Townsend Deprivation Index",
                       Grey_matter_volume_adjusted_T2 = "Grey matter volume at imaging study entry (adjusted for head size; mm^3)",
                       Grey_matter_volume_adjusted_T3  = "Grey matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T2 = "White matter volume at imaging study entry (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T3 = "White matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T2 = "Average hippocampal volume at imaging study entry (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T3 ="Average hippocampal volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Total_WMH_volume_T2 = "White matter hyperintensities volume at imaging study entry (mm^3)",
                       Total_WMH_volume_T3 = "White matter hyperintensities volume at imaging study follow-up (mm^3)"
)

CogsBrainCov.df = apply_labels(CogsBrainCov.df,
                       Age = "Age (years)",
                       BMI = "Body Mass Index (kg/m^2)",
                       Income = "Household Income",
                       Time_outdoors_summer_cont = "Time outdoors in the summer (hours/day)",
                       Time_outdoors_winter_cont = "Time outdoors in the winter (hours/day)",
                       Average_time_outdoors = "Average time outdoors (hours/day)",
                       Hearing_difficulty = "Hearing problems",
                       Eye_problems = "Eye problems",
                       Disability = "Living with a disability or long-term illness",
                       Diabetes = "Living with diabetes mellitus",
                       Cancer = "Living with or previously had cancer",
                       Other_medical_conditions = "Living with another serious medical condition",
                       CVD_problems = "Living with cardiovascular disease",
                       Clots_Asthma_Allergies = "Living with blood clots, allergies, or asthma",
                       Bipolar_Depression = "Living with Bipolar Disorder or Depression",
                       Alcohol = "Alcohol drinking status",
                       Smoking = "Smoking status",
                       Population_density = "Home area population density",
                       Summed_PA_min = "Total physical activity (min/day)",
                       Summed_walking_min = "Total walking (MET min/week)",
                       Summed_PA_MET_min = "Total physical activity (MET min/week)",
                       Trails_B_A = "Trail making test (B-A; sec)",
                       Symbol.Digit = "Symbol digit substitution test (correct matches)",
                       Greenspace_pcnt_300m = "Greenspace percentage (buffered to 300 meters)",
                       Greenspace_pcnt_1000m = "Greenspace percentage (buffered to 1000 meters)",
                       Natural_environment_pcnt_300m = "Natural environment percentage (buffered to 300 meters)",
                       Natural_environment_pcnt_1000m = "Natural environment percentage (buffered to 1000 meters)",
                       Deprivation_Index = "Townsend Deprivation Index",
                       Grey_matter_volume_adjusted_T2 = "Grey matter volume at imaging study entry (adjusted for head size; mm^3)",
                       Grey_matter_volume_adjusted_T3  = "Grey matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T2 = "White matter volume at imaging study entry (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T3 = "White matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T2 = "Average hippocampal volume at imaging study entry (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T3 ="Average hippocampal volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Total_WMH_volume_T2 = "White matter hyperintensities volume at imaging study entry (mm^3)",
                       Total_WMH_volume_T3 = "White matter hyperintensities volume at imaging study follow-up (mm^3)"
)

CogsPlusBrainCov.df = apply_labels(CogsPlusBrainCov.df,
                       Age = "Age (years)",
                       BMI = "Body Mass Index (kg/m^2)",
                       Income = "Household Income",
                       Time_outdoors_summer_cont = "Time outdoors in the summer (hours/day)",
                       Time_outdoors_winter_cont = "Time outdoors in the winter (hours/day)",
                       Average_time_outdoors = "Average time outdoors (hours/day)",
                       Hearing_difficulty = "Hearing problems",
                       Eye_problems = "Eye problems",
                       Disability = "Living with a disability or long-term illness",
                       Diabetes = "Living with diabetes mellitus",
                       Cancer = "Living with or previously had cancer",
                       Other_medical_conditions = "Living with another serious medical condition",
                       CVD_problems = "Living with cardiovascular disease",
                       Clots_Asthma_Allergies = "Living with blood clots, allergies, or asthma",
                       Bipolar_Depression = "Living with Bipolar Disorder or Depression",
                       Alcohol = "Alcohol drinking status",
                       Smoking = "Smoking status",
                       Population_density = "Home area population density",
                       Summed_PA_min = "Total physical activity (min/day)",
                       Summed_walking_min = "Total walking (MET min/week)",
                       Summed_PA_MET_min = "Total physical activity (MET min/week)",
                       Trails_B_A = "Trail making test (B-A; sec)",
                       Symbol.Digit = "Symbol digit substitution test (correct matches)",
                       Fluid_intelligence = "Fluid intelligence (correct answers)",
                       Numeric_memory = "Numeric memory (maximum digits recalled)",
                       Pairs_matching_incorrect = "Pairs matching (incorrect matches)",
                       Greenspace_pcnt_300m = "Greenspace percentage (buffered to 300 meters)",
                       Greenspace_pcnt_1000m = "Greenspace percentage (buffered to 1000 meters)",
                       Natural_environment_pcnt_300m = "Natural environment percentage (buffered to 300 meters)",
                       Natural_environment_pcnt_1000m = "Natural environment percentage (buffered to 1000 meters)",
                       Deprivation_Index = "Townsend Deprivation Index",
                       Grey_matter_volume_adjusted_T2 = "Grey matter volume at imaging study entry (adjusted for head size; mm^3)",
                       Grey_matter_volume_adjusted_T3  = "Grey matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T2 = "White matter volume at imaging study entry (adjusted for head size; mm^3)",
                       White_matter_volume_adjusted_T3 = "White matter volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T2 = "Average hippocampal volume at imaging study entry (adjusted for head size; mm^3)",
                       Avg_Hippocampal_volume_adjusted_T3 ="Average hippocampal volume at imaging study follow-up (adjusted for head size; mm^3)",
                       Total_WMH_volume_T2 = "White matter hyperintensities volume at imaging study entry (mm^3)",
                       Total_WMH_volume_T3 = "White matter hyperintensities volume at imaging study follow-up (mm^3)"
)

4) Compare the complete data set with the final cognitive+brain+covariate data set

This step will summarize participant characteristics for the full data set, as compared to the final analytical data set

Full.df$included<-"All participants"
CogsBrain.df$included<-"Participants with both brain and cognitive data" 
CogsBrainCov.df$included<-"Participants with brain, cognitive, and covariate data"

Tableone.df<-rbind(Full.df,CogsBrainCov.df)

vars<- Tableone.df %>% select(c(2:43,50))

vars %>% tbl_summary(
  statistic = list(all_continuous() ~ "{mean} ({sd})",
                   all_categorical() ~ "{n} ({p}%)"),
  digits = all_continuous() ~ 2,
  by = included
)
Characteristic All participants, N = 502,4221 Participants with brain, cognitive, and covariate data, N = 11,4481
Age (years) 56.53 (8.10) 54.95 (7.46)
    Unknown 1 0
Sex
    Female 273,332 (54%) 5,784 (51%)
    Male 229,089 (46%) 5,664 (49%)
    Unknown 1 0
Body Mass Index (kg/m^2) 27.43 (4.80) 26.38 (4.22)
    Unknown 3,105 0
Race
    Asian or Asian British 9,836 (2.0%) 81 (0.7%)
    Black or Black British 8,031 (1.6%) 52 (0.5%)
    Mixed 2,905 (0.6%) 40 (0.4%)
    White 472,055 (96%) 11,171 (98%)
    Unknown 9,595 104
Household Income
    <18,000 GBP 97,182 (20%) 1,201 (10%)
    >100,000 GBP 22,928 (4.6%) 972 (8.5%)
    18,000-30,999 GBP 108,161 (22%) 2,471 (22%)
    31,000-51,999 GBP 110,754 (22%) 3,499 (31%)
    52,000-100,000 GBP 86,251 (17%) 3,305 (29%)
    Do not know or prefer not to answer 71,134 (14%) 0 (0%)
    Unknown 6,012 0
Education
    A levels/AS levels or equivalent 55,314 (11%) 1,574 (14%)
    College or University Degree 161,132 (32%) 6,020 (53%)
    CSEs or equivalent 26,885 (5.4%) 353 (3.1%)
    National Vocational Qualification or equivalent 32,724 (6.6%) 526 (4.6%)
    None of the above 85,260 (17%) 405 (3.5%)
    O levels/General Certificate of Secondary Education or equivalent 105,178 (21%) 2,083 (18%)
    Other professional qualifications 25,799 (5.2%) 487 (4.3%)
    Prefer not to answer 5,490 (1.1%) 0 (0%)
    Unknown 4,640 0
Employment
    Doing unpaid or voluntary work 2,327 (0.5%) 55 (0.5%)
    In paid employment or self-employed 287,090 (57%) 7,878 (69%)
    Looking after home and/or family 13,855 (2.8%) 276 (2.4%)
    None of the above 2,800 (0.6%) 36 (0.3%)
    Prefer not to answer 2,079 (0.4%) 4 (<0.1%)
    Retired 166,970 (33%) 2,943 (26%)
    Student 1,343 (0.3%) 40 (0.3%)
    Unable to work because of sickness or disability 16,824 (3.4%) 86 (0.8%)
    Unemployed 8,263 (1.6%) 130 (1.1%)
    Unknown 871 0
Alcohol drinking status
    Current drinker 460,292 (92%) 10,985 (96%)
    Never 22,382 (4.5%) 227 (2.0%)
    Prefer not to answer 755 (0.2%) 1 (<0.1%)
    Previous drinker 18,095 (3.6%) 235 (2.1%)
    Unknown 898 0
Smoking status
    Current Smoker 52,963 (11%) 681 (5.9%)
    Never 273,482 (55%) 6,909 (60%)
    Prefer not to answer 2,057 (0.4%) 0 (0%)
    Previous Smoker 173,028 (35%) 3,858 (34%)
    Unknown 892 0
Living with cardiovascular disease
    No 350,901 (70%) 9,169 (80%)
    Prefer not to answer 1,293 (0.3%) 4 (<0.1%)
    Yes 149,298 (30%) 2,275 (20%)
    Unknown 930 0
Living with blood clots, allergies, or asthma
    No 339,508 (68%) 7,701 (67%)
    Prefer not to answer 1,209 (0.2%) 3 (<0.1%)
    Yes 160,773 (32%) 3,744 (33%)
    Unknown 932 0
Living with diabetes mellitus
    Don't know or prefer not to answer 1,684 (0.3%) 5 (<0.1%)
    No 473,411 (94%) 11,194 (98%)
    Yes 26,395 (5.3%) 249 (2.2%)
    Unknown 932 0
Living with or previously had cancer
    Don't know or prefer not to answer 1,843 (0.4%) 12 (0.1%)
    No 461,034 (92%) 10,806 (94%)
    Yes 38,613 (7.7%) 630 (5.5%)
    Unknown 932 0
Hearing problems
    Completely Deaf 130 (<0.1%) 0 (0%)
    Difficulty Hearing 122,021 (25%) 2,611 (23%)
    Don't know or prefer not to answer 20,275 (4.1%) 359 (3.1%)
    No Difficulty 355,307 (71%) 8,478 (74%)
    Unknown 4,689 0
Eye problems
    Do not know 4,839 (2.8%) 42 (1.0%)
    No 132,123 (76%) 3,379 (84%)
    Prefer not to answer 410 (0.2%) 2 (<0.1%)
    Yes 37,209 (21%) 590 (15%)
    Unknown 327,841 7,435
Living with a disability or long-term illness
    Don't know or prefer not to answer 12,437 (2.5%) 0 (0%)
    No 329,196 (66%) 8,825 (77%)
    Yes 159,870 (32%) 2,623 (23%)
    Unknown 919 0
Living with Bipolar Disorder or Depression
    Bipolar Disorder 1,615 (1.3%) 29 (0.9%)
    No Bipolar or Depression 89,510 (73%) 2,266 (71%)
    Probable Recurrent Major Depressive Disorder 23,907 (19%) 668 (21%)
    Probable Single Major Depressive Episode 7,922 (6.4%) 221 (6.9%)
    Unknown 379,468 8,264
Living with another serious medical condition
    Don't know or prefer not to answer 9,715 (1.9%) 110 (1.0%)
    No 391,784 (78%) 9,523 (83%)
    Yes 99,991 (20%) 1,815 (16%)
    Unknown 932 0
Total physical activity (min/day) 127.10 (101.90) 119.09 (88.94)
    Unknown 100,108 0
Total walking (MET min/week) 1,039.59 (1,086.18) 914.52 (981.18)
    Unknown 100,108 0
Total physical activity (MET min/week) 2,650.26 (2,713.19) 2,366.74 (2,285.89)
    Unknown 100,108 0
Time outdoors in the summer (hours/day) 3.80 (2.40) 3.21 (2.10)
    Unknown 33,641 0
Time outdoors in the winter (hours/day) 1.95 (1.81) 1.55 (1.36)
    Unknown 33,848 0
Average time outdoors (hours/day) 2.88 (1.93) 2.38 (1.59)
    Unknown 39,961 0
Townsend Deprivation Index 17.67 (14.02) 17.97 (14.28)
    Unknown 126,392 0
Home area population density
    Postcode not linkable 18 (<0.1%) 0 (0%)
    Town 33,850 (6.8%) 909 (7.9%)
    Urban area 428,714 (86%) 9,509 (83%)
    Village, Hamlet, or Rural Area 34,790 (7.0%) 1,030 (9.0%)
    Unknown 5,050 0
Trail making test (B-A; sec) 27.61 (20.50) 25.56 (18.38)
    Unknown 398,406 0
Symbol digit substitution test (correct matches) 19.68 (5.24) 20.67 (4.81)
    Unknown 383,971 0
Greenspace percentage (buffered to 1000 meters) 40.52 (25.60) 44.28 (26.05)
    Unknown 4,961 0
Greenspace percentage (buffered to 300 meters) 26.09 (25.10) 29.47 (26.59)
    Unknown 4,961 0
Natural environment percentage (buffered to 1000 meters) 44.99 (21.63) 47.52 (22.29)
    Unknown 61,625 0
Natural environment percentage (buffered to 300 meters) 35.27 (23.22) 37.82 (24.34)
    Unknown 61,625 0
Grey matter volume at imaging study entry (adjusted for head size; mm^3) 791,149.64 (48,503.01) 791,993.42 (47,912.11)
    Unknown 459,614 0
Grey matter volume at imaging study follow-up (adjusted for head size; mm^3) 790,640.69 (46,540.19) 789,019.68 (45,362.53)
    Unknown 498,996 10,422
White matter volume at imaging study entry (adjusted for head size; mm^3) 701,097.97 (41,152.31) 701,963.64 (40,585.11)
    Unknown 459,614 0
White matter volume at imaging study follow-up (adjusted for head size; mm^3) 696,313.45 (40,518.46) 697,239.58 (40,246.94)
    Unknown 498,996 10,422
Total_brain_volume_adjusted_T2 1,159,724.15 (111,640.01) 1,169,325.68 (109,392.72)
    Unknown 459,614 0
Total_brain_volume_adjusted_T3 1,156,133.83 (112,200.87) 1,163,884.13 (109,606.16)
    Unknown 498,996 10,422
Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 4,942.63 (579.44) 4,944.39 (574.14)
    Unknown 459,631 6
Average hippocampal volume at imaging study follow-up (adjusted for head size; mm^3) 4,965.26 (553.17) 4,931.22 (548.44)
    Unknown 499,130 10,422
White matter hyperintensities volume at imaging study entry (mm^3) 5,149.16 (6,794.83) 4,876.50 (6,376.73)
    Unknown 460,983 395
White matter hyperintensities volume at imaging study follow-up (mm^3) 5,494.23 (6,788.72) 5,451.51 (6,405.32)
    Unknown 499,010 10,427
1 Mean (SD); n (%)

Table for cognitive+brain+covariate subset, stratified by sex

tbl_summary(
  select(CogsBrainCov.df, c(2:43)),
  by = "Sex", 
  statistic = list(all_continuous() ~ "{mean} ({sd})",
                   all_categorical() ~ "{n} ({p}%)"),
  digits = all_continuous() ~ 2
) %>%
  add_p(test = list(all_continuous() ~ "t.test",
                   all_categorical() ~ "chisq.test"))
## Warning for variable 'Employment':
## simpleWarning in stats::chisq.test(x = c("In paid employment or self-employed", : Chi-squared approximation may be incorrect
## Warning for variable 'Alcohol':
## simpleWarning in stats::chisq.test(x = structure(c("Current drinker", "Current drinker", : Chi-squared approximation may be incorrect
## Warning for variable 'CVD_problems':
## simpleWarning in stats::chisq.test(x = structure(c("No", "No", "No", "No", "No", : Chi-squared approximation may be incorrect
## Warning for variable 'Clots_Asthma_Allergies':
## simpleWarning in stats::chisq.test(x = structure(c("Yes", "Yes", "No", "No", "No", : Chi-squared approximation may be incorrect
## Warning for variable 'Diabetes':
## simpleWarning in stats::chisq.test(x = structure(c("No", "No", "No", "No", "No", : Chi-squared approximation may be incorrect
## Warning for variable 'Eye_problems':
## simpleWarning in stats::chisq.test(x = structure(c(NA, NA, "No", NA, NA, NA, "Yes", : Chi-squared approximation may be incorrect
Characteristic Female, N = 5,7841 Male, N = 5,6641 p-value2
Age (years) 53.84 (7.21) 56.08 (7.54) <0.001
Body Mass Index (kg/m^2) 25.93 (4.56) 26.84 (3.78) <0.001
Race 0.13
    Asian or Asian British 33 (0.6%) 48 (0.9%)
    Black or Black British 28 (0.5%) 24 (0.4%)
    Mixed 25 (0.4%) 15 (0.3%)
    White 5,645 (98%) 5,526 (98%)
    Unknown 53 51
Household Income <0.001
    <18,000 GBP 694 (12%) 507 (9.0%)
    >100,000 GBP 471 (8.1%) 501 (8.8%)
    18,000-30,999 GBP 1,375 (24%) 1,096 (19%)
    31,000-51,999 GBP 1,733 (30%) 1,766 (31%)
    52,000-100,000 GBP 1,511 (26%) 1,794 (32%)
Education <0.001
    A levels/AS levels or equivalent 876 (15%) 698 (12%)
    College or University Degree 2,947 (51%) 3,073 (54%)
    CSEs or equivalent 173 (3.0%) 180 (3.2%)
    National Vocational Qualification or equivalent 155 (2.7%) 371 (6.6%)
    None of the above 176 (3.0%) 229 (4.0%)
    O levels/General Certificate of Secondary Education or equivalent 1,147 (20%) 936 (17%)
    Other professional qualifications 310 (5.4%) 177 (3.1%)
Employment <0.001
    Doing unpaid or voluntary work 39 (0.7%) 16 (0.3%)
    In paid employment or self-employed 4,054 (70%) 3,824 (68%)
    Looking after home and/or family 257 (4.4%) 19 (0.3%)
    None of the above 17 (0.3%) 19 (0.3%)
    Prefer not to answer 3 (<0.1%) 1 (<0.1%)
    Retired 1,297 (22%) 1,646 (29%)
    Student 23 (0.4%) 17 (0.3%)
    Unable to work because of sickness or disability 44 (0.8%) 42 (0.7%)
    Unemployed 50 (0.9%) 80 (1.4%)
Alcohol drinking status <0.001
    Current drinker 5,507 (95%) 5,478 (97%)
    Never 141 (2.4%) 86 (1.5%)
    Prefer not to answer 1 (<0.1%) 0 (0%)
    Previous drinker 135 (2.3%) 100 (1.8%)
Smoking status <0.001
    Current Smoker 297 (5.1%) 384 (6.8%)
    Never 3,667 (63%) 3,242 (57%)
    Previous Smoker 1,820 (31%) 2,038 (36%)
Living with cardiovascular disease <0.001
    No 4,904 (85%) 4,265 (75%)
    Prefer not to answer 2 (<0.1%) 2 (<0.1%)
    Yes 878 (15%) 1,397 (25%)
Living with blood clots, allergies, or asthma 0.10
    No 3,838 (66%) 3,863 (68%)
    Prefer not to answer 2 (<0.1%) 1 (<0.1%)
    Yes 1,944 (34%) 1,800 (32%)
Living with diabetes mellitus <0.001
    Don't know or prefer not to answer 3 (<0.1%) 2 (<0.1%)
    No 5,701 (99%) 5,493 (97%)
    Yes 80 (1.4%) 169 (3.0%)
Living with or previously had cancer <0.001
    Don't know or prefer not to answer 10 (0.2%) 2 (<0.1%)
    No 5,402 (93%) 5,404 (95%)
    Yes 372 (6.4%) 258 (4.6%)
Hearing problems <0.001
    Difficulty Hearing 1,110 (19%) 1,501 (27%)
    Don't know or prefer not to answer 212 (3.7%) 147 (2.6%)
    No Difficulty 4,462 (77%) 4,016 (71%)
Eye problems 0.4
    Do not know 19 (0.9%) 23 (1.1%)
    No 1,702 (85%) 1,677 (84%)
    Prefer not to answer 2 (<0.1%) 0 (0%)
    Yes 288 (14%) 302 (15%)
    Unknown 3,773 3,662
Living with a disability or long-term illness 1,203 (21%) 1,420 (25%) <0.001
Living with Bipolar Disorder or Depression <0.001
    Bipolar Disorder 15 (1.0%) 14 (0.9%)
    No Bipolar or Depression 1,013 (64%) 1,253 (78%)
    Probable Recurrent Major Depressive Disorder 426 (27%) 242 (15%)
    Probable Single Major Depressive Episode 118 (7.5%) 103 (6.4%)
    Unknown 4,212 4,052
Living with another serious medical condition 0.015
    Don't know or prefer not to answer 69 (1.2%) 41 (0.7%)
    No 4,826 (83%) 4,697 (83%)
    Yes 889 (15%) 926 (16%)
Total physical activity (min/day) 118.56 (87.26) 119.63 (90.64) 0.5
Total walking (MET min/week) 955.67 (1,008.90) 872.49 (950.28) <0.001
Total physical activity (MET min/week) 2,344.11 (2,219.79) 2,389.84 (2,351.44) 0.3
Time outdoors in the summer (hours/day) 3.01 (1.92) 3.41 (2.25) <0.001
Time outdoors in the winter (hours/day) 1.34 (1.13) 1.76 (1.54) <0.001
Average time outdoors (hours/day) 2.18 (1.37) 2.58 (1.75) <0.001
Townsend Deprivation Index 17.80 (14.39) 18.14 (14.16) 0.2
Home area population density 0.6
    Town 445 (7.7%) 464 (8.2%)
    Urban area 4,819 (83%) 4,690 (83%)
    Village, Hamlet, or Rural Area 520 (9.0%) 510 (9.0%)
Trail making test (B-A; sec) 25.11 (18.79) 26.02 (17.95) 0.009
Symbol digit substitution test (correct matches) 20.91 (5.01) 20.42 (4.58) <0.001
Greenspace percentage (buffered to 1000 meters) 43.63 (26.24) 44.94 (25.85) 0.007
Greenspace percentage (buffered to 300 meters) 29.06 (26.66) 29.90 (26.52) 0.094
Natural environment percentage (buffered to 1000 meters) 47.03 (22.45) 48.01 (22.11) 0.018
Natural environment percentage (buffered to 300 meters) 37.65 (24.49) 37.99 (24.18) 0.5
Grey matter volume at imaging study entry (adjusted for head size; mm^3) 808,447.68 (45,431.69) 775,190.56 (44,424.10) <0.001
Grey matter volume at imaging study follow-up (adjusted for head size; mm^3) 803,305.51 (43,412.76) 774,452.62 (42,628.54) <0.001
    Unknown 5,266 5,156
White matter volume at imaging study entry (adjusted for head size; mm^3) 699,249.63 (40,299.93) 704,735.15 (40,691.43) <0.001
White matter volume at imaging study follow-up (adjusted for head size; mm^3) 694,588.97 (39,844.63) 699,942.36 (40,513.84) 0.033
    Unknown 5,266 5,156
Total_brain_volume_adjusted_T2 1,113,341.30 (89,927.24) 1,226,496.17 (97,266.10) <0.001
Total_brain_volume_adjusted_T3 1,105,948.20 (85,621.28) 1,222,960.53 (99,427.20) <0.001
    Unknown 5,266 5,156
Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 5,108.73 (522.77) 4,776.51 (575.74) <0.001
    Unknown 2 4
Average hippocampal volume at imaging study follow-up (adjusted for head size; mm^3) 5,087.17 (497.40) 4,772.20 (552.84) <0.001
    Unknown 5,266 5,156
White matter hyperintensities volume at imaging study entry (mm^3) 4,283.16 (5,752.85) 5,484.30 (6,905.91) <0.001
    Unknown 191 204
White matter hyperintensities volume at imaging study follow-up (mm^3) 4,695.93 (5,419.46) 6,223.54 (7,199.99) <0.001
    Unknown 5,268 5,159
1 Mean (SD); n (%)
2 Welch Two Sample t-test; Pearson’s Chi-squared test

5) Regression analyses examining the associations of natural environment with cognitive function [subset having cognitive, brain, and covariate data]

First, this step recodes our covariates of interest into scales which are easier to interpret in a regression. Important notes: 1. Every unit of age represents 10 years above the mean age 2. Every unit of BMI represents 5 kg/m^2 above the mean BMI 3. Every unit of natural environment represents a %10 increase in natural environment 4. Brain volumes are reformatted to cubic centimeters (cm^3) 5. Education kept as nominal.

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:expss':
## 
##     compute, contains, na_if, recode, vars, where
## The following objects are masked from 'package:maditr':
## 
##     between, coalesce, first, last
## The following objects are masked from 'package:plyr':
## 
##     arrange, count, desc, failwith, id, mutate, rename, summarise,
##     summarize
## The following object is masked from 'package:MASS':
## 
##     select
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
CogsBrainCov.df2<-CogsBrainCov.df %>%
  mutate(Age = scale(Age, scale=FALSE)/10,
         Sex = recode(Sex,
                      "Female" = 0.5,
                      "Male" = -0.5),
         BMI = scale(BMI, scale=FALSE)/5,
         Race = recode(Race,
                       "White" = 0.5,
                       "Mixed" = -0.5,
                       "Black or Black British"= -0.5,
                       "Asian or Asian British"= -0.5),
         Income = as.numeric(factor(Income,
                                    levels = c("<18,000 GBP","18,000-30,999 GBP","31,000-51,999 GBP","52,000-100,000 GBP",">100,000 GBP"))),
         Disability = recode(Disability, 
                             "Yes" = 1,
                             "No" = 0),
         Diabetes = recode(Diabetes,
                           "Yes" = 1,
                           "No" = 0),
         CVD_problems = recode(CVD_problems,
                               "Yes" = 1,
                               "No" = 0),
         Cancer = recode(Cancer,
                         "Yes" = 1,
                         "No" = 0),
         Other_medical_conditions =  recode(Other_medical_conditions,
                                            "Yes" = 1,
                                            "No" = 0),
         Alcohol = as.numeric(factor(Alcohol,
                                     levels = c("Never","Previous drinker","Current drinker"))),
         Smoking = as.numeric(factor(Smoking,
                                     levels = c("Never", "Previous Smoker", "Current Smoker"))),
         Population_density = as.numeric(factor(Population_density,
                                                levels = c("Urban area", "Town", "Village, Hamlet, or Rural Area"))),
         Natural_environment_1000m_10pcnt = Natural_environment_pcnt_1000m/10,
         Greenspace_1000m_10pcnt = Greenspace_pcnt_1000m/10,
         Natural_environment_300m_10pcnt = Natural_environment_pcnt_300m/10,
         Greenspace_300m_10pcnt = Greenspace_pcnt_300m/10,
         Grey_matter_volume_adjusted_T2_cm3 = Grey_matter_volume_adjusted_T2/1000,
         White_matter_volume_adjusted_T2_cm3 = White_matter_volume_adjusted_T2/1000,
         Avg_Hippocampal_volume_adjusted_T2_cm3 = Avg_Hippocampal_volume_adjusted_T2/1000,
         Total_WMH_volume_T2_cm3 = Total_WMH_volume_T2/1000
         )
## Warning: There were 4 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `Diabetes = recode(Diabetes, Yes = 1, No = 0)`.
## Caused by warning:
## ! Unreplaced values treated as NA as `.x` is not compatible.
## Please specify replacements exhaustively or supply `.default`.
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 3 remaining warnings.
detach(package:dplyr,unload=TRUE)
## Warning: 'dplyr' namespace cannot be unloaded:
##   namespace 'dplyr' is imported by 'tidyr', 'broom.helpers', 'broom', 'gt', 'gtsummary' so cannot be unloaded

Repeating above step for separate dataset with the additional cognitive outcomes

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:expss':
## 
##     compute, contains, na_if, recode, vars, where
## The following objects are masked from 'package:maditr':
## 
##     between, coalesce, first, last
## The following objects are masked from 'package:plyr':
## 
##     arrange, count, desc, failwith, id, mutate, rename, summarise,
##     summarize
## The following object is masked from 'package:MASS':
## 
##     select
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
CogsPlusBrainCov.df2<-CogsPlusBrainCov.df %>%
  mutate(Age = scale(Age, scale=FALSE)/10,
         Sex = recode(Sex,
                      "Female" = 0.5,
                      "Male" = -0.5),
         BMI = scale(BMI, scale=FALSE)/5,
         Race = recode(Race,
                       "White" = 0.5,
                       "Mixed" = -0.5,
                       "Black or Black British"= -0.5,
                       "Asian or Asian British"= -0.5),
         Income = as.numeric(factor(Income,
                                    levels = c("<18,000 GBP","18,000-30,999 GBP","31,000-51,999 GBP","52,000-100,000 GBP",">100,000 GBP"))),
         Disability = recode(Disability, 
                             "Yes" = 1,
                             "No" = 0),
         Diabetes = recode(Diabetes,
                           "Yes" = 1,
                           "No" = 0),
         CVD_problems = recode(CVD_problems,
                               "Yes" = 1,
                               "No" = 0),
         Cancer = recode(Cancer,
                         "Yes" = 1,
                         "No" = 0),
         Other_medical_conditions =  recode(Other_medical_conditions,
                                            "Yes" = 1,
                                            "No" = 0),
         Alcohol = as.numeric(factor(Alcohol,
                                     levels = c("Never","Previous drinker","Current drinker"))),
         Smoking = as.numeric(factor(Smoking,
                                     levels = c("Never", "Previous Smoker", "Current Smoker"))),
         Population_density = as.numeric(factor(Population_density,
                                                levels = c("Urban area", "Town", "Village, Hamlet, or Rural Area"))),
         Natural_environment_1000m_10pcnt = Natural_environment_pcnt_1000m/10,
         Greenspace_1000m_10pcnt = Greenspace_pcnt_1000m/10,
         Natural_environment_300m_10pcnt = Natural_environment_pcnt_300m/10,
         Greenspace_300m_10pcnt = Greenspace_pcnt_300m/10,
         Grey_matter_volume_adjusted_T2_cm3 = Grey_matter_volume_adjusted_T2/1000,
         White_matter_volume_adjusted_T2_cm3 = White_matter_volume_adjusted_T2/1000,
         Avg_Hippocampal_volume_adjusted_T2_cm3 = Avg_Hippocampal_volume_adjusted_T2/1000,
         Total_WMH_volume_T2_cm3 = Total_WMH_volume_T2/1000
         )
## Warning: There were 4 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `Diabetes = recode(Diabetes, Yes = 1, No = 0)`.
## Caused by warning:
## ! Unreplaced values treated as NA as `.x` is not compatible.
## Please specify replacements exhaustively or supply `.default`.
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 3 remaining warnings.
detach(package:dplyr,unload=TRUE)
## Warning: 'dplyr' namespace cannot be unloaded:
##   namespace 'dplyr' is imported by 'tidyr', 'broom.helpers', 'broom', 'gt', 'gtsummary' so cannot be unloaded

Define function to get both model summary and confidence interval

summary_confint <- function(model) {
  list(summary(model), confint(model))
  }

Define function for regression model assumption checks

# Install package for Durbin-Watson test
options(repos = c(CRAN = "https://cran.r-project.org"))
install.packages(c("lmtest", "gvlma"))
## 
## The downloaded binary packages are in
##  /var/folders/4k/nmtv694x34xfs4q3zzfbb42c0000gn/T//RtmpMn7uoA/downloaded_packages
library("lmtest")
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library("gvlma")

model_diagnostics <- function(model, bin_width=1) {
  # Residuals vs. Fitted plot for linearity, normality, equivariance
  # Normal Q-Q plot for normality
  # Residuals vs. Leverage plot for influential outliers
  plot(model, which = c(1,2,5))

  # Histogram of residuals for normality
  hist(residuals(model), breaks = seq(floor(min(residuals(model))), ceiling(max(residuals(model))), by = bin_width))
  
  # Durbin-Watson test for independent errors
  print(dwtest(model))
  
  # Test skewness, kurtosis, equivariance
  gvlma(model)
  
  # Test multicollinearity among predictors (in interaction models) and among covariates?
  #vif(model)
}

5.1) 1000m buffer for natural environment percentage

5.1.1) Models for the association of natural environment with trail making test (B-A)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(Trails_B_A~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.826, -10.244, -2.518, 6.972, 176.386
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                28.03101
## Natural_environment_1000m_10pcnt                                           -0.13556
## Age                                                                         4.20655
## Sex                                                                         0.11482
## BMI                                                                         0.14804
## EducationCollege or University Degree                                      -0.62606
## EducationCSEs or equivalent                                                 4.52109
## EducationNational Vocational Qualification or equivalent                    7.07579
## EducationNone of the above                                                 10.33207
## EducationO levels/General Certificate of Secondary Education or equivalent  1.83526
## EducationOther professional qualifications                                  3.61424
## Income                                                                     -0.92886
##                                                                            Std. Error
## (Intercept)                                                                   0.74431
## Natural_environment_1000m_10pcnt                                              0.07472
## Age                                                                           0.23833
## Sex                                                                           0.34262
## BMI                                                                           0.19886
## EducationCollege or University Degree                                         0.50707
## EducationCSEs or equivalent                                                   1.05004
## EducationNational Vocational Qualification or equivalent                      0.90017
## EducationNone of the above                                                    1.00489
## EducationO levels/General Certificate of Secondary Education or equivalent    0.59534
## EducationOther professional qualifications                                    0.92460
## Income                                                                        0.16232
##                                                                            t value
## (Intercept)                                                                 37.661
## Natural_environment_1000m_10pcnt                                            -1.814
## Age                                                                         17.650
## Sex                                                                          0.335
## BMI                                                                          0.744
## EducationCollege or University Degree                                       -1.235
## EducationCSEs or equivalent                                                  4.306
## EducationNational Vocational Qualification or equivalent                     7.861
## EducationNone of the above                                                  10.282
## EducationO levels/General Certificate of Secondary Education or equivalent   3.083
## EducationOther professional qualifications                                   3.909
## Income                                                                      -5.722
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.06967
## Age                                                                         < 2e-16
## Sex                                                                         0.73753
## BMI                                                                         0.45662
## EducationCollege or University Degree                                       0.21698
## EducationCSEs or equivalent                                                1.68e-05
## EducationNational Vocational Qualification or equivalent                   4.17e-15
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00206
## EducationOther professional qualifications                                 9.32e-05
## Income                                                                     1.08e-08
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           .  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.74 on 11436 degrees of freedom
## Multiple R-squared:  0.06947,    Adjusted R-squared:  0.06857 
## F-statistic: 77.61 on 11 and 11436 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

model5b1 <- lm(Trails_B_A~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors +  
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model5b1)
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -135.169, -10.202, -2.522, 6.951, 175.454
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.319623
## Natural_environment_1000m_10pcnt                                           -0.197120
## Age                                                                         4.104806
## Sex                                                                         0.264749
## BMI                                                                         0.186970
## EducationCollege or University Degree                                      -0.524792
## EducationCSEs or equivalent                                                 4.177148
## EducationNational Vocational Qualification or equivalent                    6.827414
## EducationNone of the above                                                  9.856431
## EducationO levels/General Certificate of Secondary Education or equivalent  1.704935
## EducationOther professional qualifications                                  3.547735
## Income                                                                     -0.843623
## Average_time_outdoors                                                       0.302325
## Summed_PA_min                                                               0.003392
## Smoking                                                                     0.640837
## Disability                                                                 -0.065834
## Deprivation_Index                                                          -0.037773
## Population_density                                                          0.313549
##                                                                            Std. Error
## (Intercept)                                                                  0.956701
## Natural_environment_1000m_10pcnt                                             0.100993
## Age                                                                          0.240122
## Sex                                                                          0.345732
## BMI                                                                          0.201118
## EducationCollege or University Degree                                        0.507443
## EducationCSEs or equivalent                                                  1.052248
## EducationNational Vocational Qualification or equivalent                     0.900846
## EducationNone of the above                                                   1.009772
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595634
## EducationOther professional qualifications                                   0.924042
## Income                                                                       0.164391
## Average_time_outdoors                                                        0.117249
## Summed_PA_min                                                                0.002020
## Smoking                                                                      0.277485
## Disability                                                                   0.399969
## Deprivation_Index                                                            0.011608
## Population_density                                                           0.368474
##                                                                            t value
## (Intercept)                                                                 27.511
## Natural_environment_1000m_10pcnt                                            -1.952
## Age                                                                         17.095
## Sex                                                                          0.766
## BMI                                                                          0.930
## EducationCollege or University Degree                                       -1.034
## EducationCSEs or equivalent                                                  3.970
## EducationNational Vocational Qualification or equivalent                     7.579
## EducationNone of the above                                                   9.761
## EducationO levels/General Certificate of Secondary Education or equivalent   2.862
## EducationOther professional qualifications                                   3.839
## Income                                                                      -5.132
## Average_time_outdoors                                                        2.578
## Summed_PA_min                                                                1.679
## Smoking                                                                      2.309
## Disability                                                                  -0.165
## Deprivation_Index                                                           -3.254
## Population_density                                                           0.851
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.050984
## Age                                                                         < 2e-16
## Sex                                                                        0.443832
## BMI                                                                        0.352571
## EducationCollege or University Degree                                      0.301070
## EducationCSEs or equivalent                                                7.24e-05
## EducationNational Vocational Qualification or equivalent                   3.75e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004212
## EducationOther professional qualifications                                 0.000124
## Income                                                                     2.92e-07
## Average_time_outdoors                                                      0.009936
## Summed_PA_min                                                              0.093248
## Smoking                                                                    0.020937
## Disability                                                                 0.869263
## Deprivation_Index                                                          0.001141
## Population_density                                                         0.394821
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           .  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11430 degrees of freedom
## Multiple R-squared:  0.07202,    Adjusted R-squared:  0.07064 
## F-statistic: 52.18 on 17 and 11430 DF,  p-value: < 2.2e-16
confint(model5b1,"Natural_environment_1000m_10pcnt") #95% confidence interval
##                                       2.5 %       97.5 %
## Natural_environment_1000m_10pcnt -0.3950822 0.0008430974

Model assumption checks

model_diagnostics(model5b1)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9622, p-value = 0.02151
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  26.319623  
##                                           Natural_environment_1000m_10pcnt  
##                                                                  -0.197120  
##                                                                        Age  
##                                                                   4.104806  
##                                                                        Sex  
##                                                                   0.264749  
##                                                                        BMI  
##                                                                   0.186970  
##                                      EducationCollege or University Degree  
##                                                                  -0.524792  
##                                                EducationCSEs or equivalent  
##                                                                   4.177148  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                   6.827414  
##                                                 EducationNone of the above  
##                                                                   9.856431  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                   1.704935  
##                                 EducationOther professional qualifications  
##                                                                   3.547735  
##                                                                     Income  
##                                                                  -0.843623  
##                                                      Average_time_outdoors  
##                                                                   0.302325  
##                                                              Summed_PA_min  
##                                                                   0.003392  
##                                                                    Smoking  
##                                                                   0.640837  
##                                                                 Disability  
##                                                                  -0.065834  
##                                                          Deprivation_Index  
##                                                                  -0.037773  
##                                                         Population_density  
##                                                                   0.313549  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                       Value   p-value                   Decision
## Global Stat        33417.89 0.000e+00 Assumptions NOT satisfied!
## Skewness            3888.10 0.000e+00 Assumptions NOT satisfied!
## Kurtosis           29462.90 0.000e+00 Assumptions NOT satisfied!
## Link Function         42.34 7.659e-11 Assumptions NOT satisfied!
## Heteroscedasticity    24.54 7.270e-07 Assumptions NOT satisfied!
  # Residuals vs. Fitted plot suggests approximately linear, minor heteroskedasticity
  # Normal Q-Q plot suggests non-normal skew
  # Residuals vs. Leverage plot: no outliers of major concern
  # Histogram of residuals: approximately normal, maybe slight positive skew
  # Durbin-Watson test near 2 suggests independent residuals
  # Skewness, Kurtosis, and Heteroskedasticity tests suggest non-normal and heteroskedastic

5.1.2) Models for the association of natural environment with Symbol Digit Substitution test

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(Symbol.Digit~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.396, -2.478, 0.297, 2.805, 63.13
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                19.356208
## Natural_environment_1000m_10pcnt                                            0.070807
## Age                                                                        -2.414212
## Sex                                                                         0.020358
## BMI                                                                         0.002831
## EducationCollege or University Degree                                       0.310574
## EducationCSEs or equivalent                                                -1.306249
## EducationNational Vocational Qualification or equivalent                   -0.894890
## EducationNone of the above                                                 -1.596697
## EducationO levels/General Certificate of Secondary Education or equivalent -0.460649
## EducationOther professional qualifications                                 -1.144700
## Income                                                                      0.356857
##                                                                            Std. Error
## (Intercept)                                                                  0.181365
## Natural_environment_1000m_10pcnt                                             0.018207
## Age                                                                          0.058075
## Sex                                                                          0.083486
## BMI                                                                          0.048457
## EducationCollege or University Degree                                        0.123557
## EducationCSEs or equivalent                                                  0.255864
## EducationNational Vocational Qualification or equivalent                     0.219343
## EducationNone of the above                                                   0.244862
## EducationO levels/General Certificate of Secondary Education or equivalent   0.145066
## EducationOther professional qualifications                                   0.225297
## Income                                                                       0.039552
##                                                                            t value
## (Intercept)                                                                106.725
## Natural_environment_1000m_10pcnt                                             3.889
## Age                                                                        -41.571
## Sex                                                                          0.244
## BMI                                                                          0.058
## EducationCollege or University Degree                                        2.514
## EducationCSEs or equivalent                                                 -5.105
## EducationNational Vocational Qualification or equivalent                    -4.080
## EducationNone of the above                                                  -6.521
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.175
## EducationOther professional qualifications                                  -5.081
## Income                                                                       9.022
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.000101
## Age                                                                         < 2e-16
## Sex                                                                        0.807354
## BMI                                                                        0.953417
## EducationCollege or University Degree                                      0.011963
## EducationCSEs or equivalent                                                3.36e-07
## EducationNational Vocational Qualification or equivalent                   4.54e-05
## EducationNone of the above                                                 7.29e-11
## EducationO levels/General Certificate of Secondary Education or equivalent 0.001500
## EducationOther professional qualifications                                 3.82e-07
## Income                                                                      < 2e-16
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.323 on 11436 degrees of freedom
## Multiple R-squared:  0.1922, Adjusted R-squared:  0.1914 
## F-statistic: 247.4 on 11 and 11436 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

model5b2 <- lm(Symbol.Digit~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model5b2)
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.823, -2.476, 0.287, 2.77, 63.417
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.4024640
## Natural_environment_1000m_10pcnt                                            0.1055849
## Age                                                                        -2.3518928
## Sex                                                                        -0.0683867
## BMI                                                                        -0.0050795
## EducationCollege or University Degree                                       0.2697075
## EducationCSEs or equivalent                                                -1.1339993
## EducationNational Vocational Qualification or equivalent                   -0.7894064
## EducationNone of the above                                                 -1.3717197
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3958102
## EducationOther professional qualifications                                 -1.0853782
## Income                                                                      0.3084838
## Average_time_outdoors                                                      -0.1830629
## Summed_PA_min                                                              -0.0014703
## Smoking                                                                    -0.1330314
## Disability                                                                 -0.2396478
## Deprivation_Index                                                          -0.0013019
## Population_density                                                         -0.1532552
##                                                                            Std. Error
## (Intercept)                                                                 0.2325660
## Natural_environment_1000m_10pcnt                                            0.0245504
## Age                                                                         0.0583716
## Sex                                                                         0.0840445
## BMI                                                                         0.0488902
## EducationCollege or University Degree                                       0.1233552
## EducationCSEs or equivalent                                                 0.2557926
## EducationNational Vocational Qualification or equivalent                    0.2189881
## EducationNone of the above                                                  0.2454671
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1447935
## EducationOther professional qualifications                                  0.2246268
## Income                                                                      0.0399619
## Average_time_outdoors                                                       0.0285023
## Summed_PA_min                                                               0.0004912
## Smoking                                                                     0.0674543
## Disability                                                                  0.0972290
## Deprivation_Index                                                           0.0028219
## Population_density                                                          0.0895729
##                                                                            t value
## (Intercept)                                                                 87.728
## Natural_environment_1000m_10pcnt                                             4.301
## Age                                                                        -40.292
## Sex                                                                         -0.814
## BMI                                                                         -0.104
## EducationCollege or University Degree                                        2.186
## EducationCSEs or equivalent                                                 -4.433
## EducationNational Vocational Qualification or equivalent                    -3.605
## EducationNone of the above                                                  -5.588
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.734
## EducationOther professional qualifications                                  -4.832
## Income                                                                       7.719
## Average_time_outdoors                                                       -6.423
## Summed_PA_min                                                               -2.993
## Smoking                                                                     -1.972
## Disability                                                                  -2.465
## Deprivation_Index                                                           -0.461
## Population_density                                                          -1.711
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           1.72e-05
## Age                                                                         < 2e-16
## Sex                                                                        0.415836
## BMI                                                                        0.917254
## EducationCollege or University Degree                                      0.028804
## EducationCSEs or equivalent                                                9.37e-06
## EducationNational Vocational Qualification or equivalent                   0.000314
## EducationNone of the above                                                 2.35e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.006274
## EducationOther professional qualifications                                 1.37e-06
## Income                                                                     1.27e-14
## Average_time_outdoors                                                      1.39e-10
## Summed_PA_min                                                              0.002765
## Smoking                                                                    0.048614
## Disability                                                                 0.013724
## Deprivation_Index                                                          0.644537
## Population_density                                                         0.087117
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                         .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.308 on 11430 degrees of freedom
## Multiple R-squared:  0.1982, Adjusted R-squared:  0.197 
## F-statistic: 166.2 on 17 and 11430 DF,  p-value: < 2.2e-16
confint(model5b2,"Natural_environment_1000m_10pcnt") #95% confidence interval
##                                       2.5 %    97.5 %
## Natural_environment_1000m_10pcnt 0.05746182 0.1537079

Line graph illustration of the full adjusted model * Note: change of natural environment variable (not divided into 10% increments)

mdl.3<-resid(lm(Symbol.Digit~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

mdl.4<-resid(lm(Natural_environment_pcnt_1000m~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

Symbol.Digit.graph<-as.data.frame(cbind(mdl.3,mdl.4))
Symbol.Digit.graph$mdl.3<-Symbol.Digit.graph$mdl.3 + mean(CogsBrainCov.df2$Symbol.Digit)
Symbol.Digit.graph$mdl.4<-Symbol.Digit.graph$mdl.4 + mean(CogsBrainCov.df2$Natural_environment_pcnt_1000m)


ggplot(data = Symbol.Digit.graph, aes(x = mdl.4, y = mdl.3)) + 
  labs(x="Natural Environment (%)", y="Symbol Digit Substitution Test (correct matches)")  + geom_smooth(method= 'lm',  se = TRUE, color= 'black') +
  xlim(0,100) +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
                     panel.grid.minor = element_blank(), axis.line = element_line(colour = "black"))
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 10 rows containing non-finite values (`stat_smooth()`).

Model assumption checks

model_diagnostics(model5b2)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9756, p-value = 0.09619
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  20.402464  
##                                           Natural_environment_1000m_10pcnt  
##                                                                   0.105585  
##                                                                        Age  
##                                                                  -2.351893  
##                                                                        Sex  
##                                                                  -0.068387  
##                                                                        BMI  
##                                                                  -0.005079  
##                                      EducationCollege or University Degree  
##                                                                   0.269708  
##                                                EducationCSEs or equivalent  
##                                                                  -1.133999  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  -0.789406  
##                                                 EducationNone of the above  
##                                                                  -1.371720  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  -0.395810  
##                                 EducationOther professional qualifications  
##                                                                  -1.085378  
##                                                                     Income  
##                                                                   0.308484  
##                                                      Average_time_outdoors  
##                                                                  -0.183063  
##                                                              Summed_PA_min  
##                                                                  -0.001470  
##                                                                    Smoking  
##                                                                  -0.133031  
##                                                                 Disability  
##                                                                  -0.239648  
##                                                          Deprivation_Index  
##                                                                  -0.001302  
##                                                         Population_density  
##                                                                  -0.153255  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                        Value p-value                   Decision
## Global Stat        1.441e+04  0.0000 Assumptions NOT satisfied!
## Skewness           2.055e+02  0.0000 Assumptions NOT satisfied!
## Kurtosis           1.420e+04  0.0000 Assumptions NOT satisfied!
## Link Function      5.842e-02  0.8090    Assumptions acceptable.
## Heteroscedasticity 2.878e+00  0.0898    Assumptions acceptable.
  # Residuals vs. Fitted plot suggests approximately linear, some heteroskedasticity, 1 outlier
  # Normal Q-Q plot suggests non-normal skew, 1 outlier
  # Residuals vs. Leverage plot: 1 clear outlier
  # Histogram of residuals: approximately normal, slight negative skew
  # Durbin-Watson test near 2 suggests independent residuals
  # Skewness, Kurtosis, and Heteroskedasticity tests suggest non-normal but homoskedastic

5.2) 300m buffer for natural environment percentage

5.2.1) Association of natural environment with Trail-making Test (B-A) (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(Trails_B_A~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Age + 
##     Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.634, -10.245, -2.541, 6.941, 176.355
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                27.70011
## Natural_environment_300m_10pcnt                                            -0.08815
## Age                                                                         4.19754
## Sex                                                                         0.12464
## BMI                                                                         0.14704
## EducationCollege or University Degree                                      -0.60437
## EducationCSEs or equivalent                                                 4.52316
## EducationNational Vocational Qualification or equivalent                    7.07816
## EducationNone of the above                                                 10.34214
## EducationO levels/General Certificate of Secondary Education or equivalent  1.83311
## EducationOther professional qualifications                                  3.60920
## Income                                                                     -0.92597
##                                                                            Std. Error
## (Intercept)                                                                   0.69798
## Natural_environment_300m_10pcnt                                               0.06834
## Age                                                                           0.23829
## Sex                                                                           0.34262
## BMI                                                                           0.19888
## EducationCollege or University Degree                                         0.50686
## EducationCSEs or equivalent                                                   1.05012
## EducationNational Vocational Qualification or equivalent                      0.90025
## EducationNone of the above                                                    1.00495
## EducationO levels/General Certificate of Secondary Education or equivalent    0.59540
## EducationOther professional qualifications                                    0.92468
## Income                                                                        0.16249
##                                                                            t value
## (Intercept)                                                                 39.686
## Natural_environment_300m_10pcnt                                             -1.290
## Age                                                                         17.615
## Sex                                                                          0.364
## BMI                                                                          0.739
## EducationCollege or University Degree                                       -1.192
## EducationCSEs or equivalent                                                  4.307
## EducationNational Vocational Qualification or equivalent                     7.862
## EducationNone of the above                                                  10.291
## EducationO levels/General Certificate of Secondary Education or equivalent   3.079
## EducationOther professional qualifications                                   3.903
## Income                                                                      -5.699
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.19713
## Age                                                                         < 2e-16
## Sex                                                                         0.71604
## BMI                                                                         0.45970
## EducationCollege or University Degree                                       0.23314
## EducationCSEs or equivalent                                                1.67e-05
## EducationNational Vocational Qualification or equivalent                   4.11e-15
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00208
## EducationOther professional qualifications                                 9.55e-05
## Income                                                                     1.24e-08
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.74 on 11436 degrees of freedom
## Multiple R-squared:  0.06933,    Adjusted R-squared:  0.06844 
## F-statistic: 77.45 on 11 and 11436 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Age + 
##     Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.921, -10.238, -2.519, 6.92, 175.4
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                25.978405
## Natural_environment_300m_10pcnt                                            -0.120458
## Age                                                                         4.099085
## Sex                                                                         0.282044
## BMI                                                                         0.181500
## EducationCollege or University Degree                                      -0.491296
## EducationCSEs or equivalent                                                 4.177054
## EducationNational Vocational Qualification or equivalent                    6.826067
## EducationNone of the above                                                  9.862549
## EducationO levels/General Certificate of Secondary Education or equivalent  1.699130
## EducationOther professional qualifications                                  3.542544
## Income                                                                     -0.833782
## Average_time_outdoors                                                       0.303022
## Summed_PA_min                                                               0.003354
## Smoking                                                                     0.659077
## Disability                                                                 -0.058995
## Deprivation_Index                                                          -0.037928
## Population_density                                                          0.147731
##                                                                            Std. Error
## (Intercept)                                                                  0.935984
## Natural_environment_300m_10pcnt                                              0.090910
## Age                                                                          0.240111
## Sex                                                                          0.345656
## BMI                                                                          0.201100
## EducationCollege or University Degree                                        0.507016
## EducationCSEs or equivalent                                                  1.052345
## EducationNational Vocational Qualification or equivalent                     0.900971
## EducationNone of the above                                                   1.009887
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595707
## EducationOther professional qualifications                                   0.924137
## Income                                                                       0.164403
## Average_time_outdoors                                                        0.117292
## Summed_PA_min                                                                0.002021
## Smoking                                                                      0.277219
## Disability                                                                   0.400010
## Deprivation_Index                                                            0.011609
## Population_density                                                           0.362945
##                                                                            t value
## (Intercept)                                                                 27.755
## Natural_environment_300m_10pcnt                                             -1.325
## Age                                                                         17.072
## Sex                                                                          0.816
## BMI                                                                          0.903
## EducationCollege or University Degree                                       -0.969
## EducationCSEs or equivalent                                                  3.969
## EducationNational Vocational Qualification or equivalent                     7.576
## EducationNone of the above                                                   9.766
## EducationO levels/General Certificate of Secondary Education or equivalent   2.852
## EducationOther professional qualifications                                   3.833
## Income                                                                      -5.072
## Average_time_outdoors                                                        2.583
## Summed_PA_min                                                                1.660
## Smoking                                                                      2.377
## Disability                                                                  -0.147
## Deprivation_Index                                                           -3.267
## Population_density                                                           0.407
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.185188
## Age                                                                         < 2e-16
## Sex                                                                        0.414536
## BMI                                                                        0.366791
## EducationCollege or University Degree                                      0.332568
## EducationCSEs or equivalent                                                7.25e-05
## EducationNational Vocational Qualification or equivalent                   3.83e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004348
## EducationOther professional qualifications                                 0.000127
## Income                                                                     4.01e-07
## Average_time_outdoors                                                      0.009793
## Summed_PA_min                                                              0.096930
## Smoking                                                                    0.017449
## Disability                                                                 0.882752
## Deprivation_Index                                                          0.001090
## Population_density                                                         0.683990
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11430 degrees of freedom
## Multiple R-squared:  0.07185,    Adjusted R-squared:  0.07047 
## F-statistic: 52.05 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.1437167009
## Natural_environment_300m_10pcnt                                            -0.2986579004
## Age                                                                         3.6284272059
## Sex                                                                        -0.3955017096
## BMI                                                                        -0.2126906106
## EducationCollege or University Degree                                      -1.4851343887
## EducationCSEs or equivalent                                                 2.1142776700
## EducationNational Vocational Qualification or equivalent                    5.0600084976
## EducationNone of the above                                                  7.8829969691
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5314426456
## EducationOther professional qualifications                                  1.7310764101
## Income                                                                     -1.1560405779
## Average_time_outdoors                                                       0.0731091691
## Summed_PA_min                                                              -0.0006063779
## Smoking                                                                     0.1156794342
## Disability                                                                 -0.8430827522
## Deprivation_Index                                                          -0.0606834097
## Population_density                                                         -0.5637034118
##                                                                                  97.5 %
## (Intercept)                                                                27.813093252
## Natural_environment_300m_10pcnt                                             0.057740941
## Age                                                                         4.569742935
## Sex                                                                         0.959589563
## BMI                                                                         0.575691568
## EducationCollege or University Degree                                       0.502541554
## EducationCSEs or equivalent                                                 6.239830157
## EducationNational Vocational Qualification or equivalent                    8.592125397
## EducationNone of the above                                                 11.842100826
## EducationO levels/General Certificate of Secondary Education or equivalent  2.866817616
## EducationOther professional qualifications                                  5.354012098
## Income                                                                     -0.511523401
## Average_time_outdoors                                                       0.532935690
## Summed_PA_min                                                               0.007314745
## Smoking                                                                     1.202474121
## Disability                                                                  0.725092504
## Deprivation_Index                                                          -0.015172380
## Population_density                                                          0.859165814

Model assumption checks

model_diagnostics(lm(Trails_B_A~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9623, p-value = 0.02181
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Age + 
##     Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  25.978405  
##                                            Natural_environment_300m_10pcnt  
##                                                                  -0.120458  
##                                                                        Age  
##                                                                   4.099085  
##                                                                        Sex  
##                                                                   0.282044  
##                                                                        BMI  
##                                                                   0.181500  
##                                      EducationCollege or University Degree  
##                                                                  -0.491296  
##                                                EducationCSEs or equivalent  
##                                                                   4.177054  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                   6.826067  
##                                                 EducationNone of the above  
##                                                                   9.862549  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                   1.699130  
##                                 EducationOther professional qualifications  
##                                                                   3.542544  
##                                                                     Income  
##                                                                  -0.833782  
##                                                      Average_time_outdoors  
##                                                                   0.303022  
##                                                              Summed_PA_min  
##                                                                   0.003354  
##                                                                    Smoking  
##                                                                   0.659077  
##                                                                 Disability  
##                                                                  -0.058995  
##                                                          Deprivation_Index  
##                                                                  -0.037928  
##                                                         Population_density  
##                                                                   0.147731  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                       Value   p-value                   Decision
## Global Stat        33392.58 0.000e+00 Assumptions NOT satisfied!
## Skewness            3888.88 0.000e+00 Assumptions NOT satisfied!
## Kurtosis           29436.47 0.000e+00 Assumptions NOT satisfied!
## Link Function         42.87 5.843e-11 Assumptions NOT satisfied!
## Heteroscedasticity    24.37 7.968e-07 Assumptions NOT satisfied!
  # Residuals vs. Fitted plot 
  # Normal Q-Q plot 
  # Residuals vs. Leverage plot
  # Histogram of residuals
  # Durbin-Watson test 
  # Skewness, Kurtosis, and Heteroskedasticity tests 

5.2.2) Association of natural environment with Symbol Digit Substitution (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.368, -2.485, 0.298, 2.814, 63.194
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                19.558084
## Natural_environment_300m_10pcnt                                             0.037574
## Age                                                                        -2.407839
## Sex                                                                         0.015427
## BMI                                                                         0.003275
## EducationCollege or University Degree                                       0.298274
## EducationCSEs or equivalent                                                -1.307168
## EducationNational Vocational Qualification or equivalent                   -0.895226
## EducationNone of the above                                                 -1.601994
## EducationO levels/General Certificate of Secondary Education or equivalent -0.458474
## EducationOther professional qualifications                                 -1.140415
## Income                                                                      0.356403
##                                                                            Std. Error
## (Intercept)                                                                  0.170139
## Natural_environment_300m_10pcnt                                              0.016659
## Age                                                                          0.058085
## Sex                                                                          0.083517
## BMI                                                                          0.048478
## EducationCollege or University Degree                                        0.123552
## EducationCSEs or equivalent                                                  0.255976
## EducationNational Vocational Qualification or equivalent                     0.219444
## EducationNone of the above                                                   0.244965
## EducationO levels/General Certificate of Secondary Education or equivalent   0.145134
## EducationOther professional qualifications                                   0.225400
## Income                                                                       0.039609
##                                                                            t value
## (Intercept)                                                                114.954
## Natural_environment_300m_10pcnt                                              2.255
## Age                                                                        -41.454
## Sex                                                                          0.185
## BMI                                                                          0.068
## EducationCollege or University Degree                                        2.414
## EducationCSEs or equivalent                                                 -5.107
## EducationNational Vocational Qualification or equivalent                    -4.080
## EducationNone of the above                                                  -6.540
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.159
## EducationOther professional qualifications                                  -5.060
## Income                                                                       8.998
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.02412
## Age                                                                         < 2e-16
## Sex                                                                         0.85346
## BMI                                                                         0.94613
## EducationCollege or University Degree                                       0.01579
## EducationCSEs or equivalent                                                3.33e-07
## EducationNational Vocational Qualification or equivalent                   4.54e-05
## EducationNone of the above                                                 6.43e-11
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00159
## EducationOther professional qualifications                                 4.27e-07
## Income                                                                      < 2e-16
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.325 on 11436 degrees of freedom
## Multiple R-squared:  0.1915, Adjusted R-squared:  0.1907 
## F-statistic: 246.2 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                19.224583325
## Natural_environment_300m_10pcnt                                             0.004919051
## Age                                                                        -2.521695124
## Sex                                                                        -0.148280440
## BMI                                                                        -0.091749867
## EducationCollege or University Degree                                       0.056091526
## EducationCSEs or equivalent                                                -1.808924932
## EducationNational Vocational Qualification or equivalent                   -1.325373874
## EducationNone of the above                                                 -2.082167681
## EducationO levels/General Certificate of Secondary Education or equivalent -0.742961648
## EducationOther professional qualifications                                 -1.582237399
## Income                                                                      0.278762933
##                                                                                 97.5 %
## (Intercept)                                                                19.89158554
## Natural_environment_300m_10pcnt                                             0.07022844
## Age                                                                        -2.29398363
## Sex                                                                         0.17913388
## BMI                                                                         0.09830077
## EducationCollege or University Degree                                       0.54045631
## EducationCSEs or equivalent                                                -0.80541136
## EducationNational Vocational Qualification or equivalent                   -0.46507758
## EducationNone of the above                                                 -1.12182102
## EducationO levels/General Certificate of Secondary Education or equivalent -0.17398583
## EducationOther professional qualifications                                 -0.69859263
## Income                                                                      0.43404344

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.747, -2.478, 0.28, 2.778, 63.542
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.5922670
## Natural_environment_300m_10pcnt                                             0.0488907
## Age                                                                        -2.3482647
## Sex                                                                        -0.0775818
## BMI                                                                        -0.0015217
## EducationCollege or University Degree                                       0.2499582
## EducationCSEs or equivalent                                                -1.1334265
## EducationNational Vocational Qualification or equivalent                   -0.7864392
## EducationNone of the above                                                 -1.3737571
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3905807
## EducationOther professional qualifications                                 -1.0806146
## Income                                                                      0.3037178
## Average_time_outdoors                                                      -0.1828565
## Summed_PA_min                                                              -0.0014475
## Smoking                                                                    -0.1446379
## Disability                                                                 -0.2428538
## Deprivation_Index                                                          -0.0012142
## Population_density                                                         -0.0234249
##                                                                            Std. Error
## (Intercept)                                                                 0.2276446
## Natural_environment_300m_10pcnt                                             0.0221106
## Age                                                                         0.0583983
## Sex                                                                         0.0840685
## BMI                                                                         0.0489105
## EducationCollege or University Degree                                       0.1233135
## EducationCSEs or equivalent                                                 0.2559453
## EducationNational Vocational Qualification or equivalent                    0.2191291
## EducationNone of the above                                                  0.2456190
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1448844
## EducationOther professional qualifications                                  0.2247634
## Income                                                                      0.0399852
## Average_time_outdoors                                                       0.0285272
## Summed_PA_min                                                               0.0004914
## Smoking                                                                     0.0674237
## Disability                                                                  0.0972881
## Deprivation_Index                                                           0.0028235
## Population_density                                                          0.0882734
##                                                                            t value
## (Intercept)                                                                 90.458
## Natural_environment_300m_10pcnt                                              2.211
## Age                                                                        -40.211
## Sex                                                                         -0.923
## BMI                                                                         -0.031
## EducationCollege or University Degree                                        2.027
## EducationCSEs or equivalent                                                 -4.428
## EducationNational Vocational Qualification or equivalent                    -3.589
## EducationNone of the above                                                  -5.593
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.696
## EducationOther professional qualifications                                  -4.808
## Income                                                                       7.596
## Average_time_outdoors                                                       -6.410
## Summed_PA_min                                                               -2.945
## Smoking                                                                     -2.145
## Disability                                                                  -2.496
## Deprivation_Index                                                           -0.430
## Population_density                                                          -0.265
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.027043
## Age                                                                         < 2e-16
## Sex                                                                        0.356110
## BMI                                                                        0.975180
## EducationCollege or University Degree                                      0.042684
## EducationCSEs or equivalent                                                9.58e-06
## EducationNational Vocational Qualification or equivalent                   0.000333
## EducationNone of the above                                                 2.28e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.007032
## EducationOther professional qualifications                                 1.55e-06
## Income                                                                     3.30e-14
## Average_time_outdoors                                                      1.51e-10
## Summed_PA_min                                                              0.003231
## Smoking                                                                    0.031957
## Disability                                                                 0.012566
## Deprivation_Index                                                          0.667178
## Population_density                                                         0.790732
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.311 on 11430 degrees of freedom
## Multiple R-squared:  0.1973, Adjusted R-squared:  0.1961 
## F-statistic: 165.2 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.146044589
## Natural_environment_300m_10pcnt                                             0.005550060
## Age                                                                        -2.462735434
## Sex                                                                        -0.242370614
## BMI                                                                        -0.097394630
## EducationCollege or University Degree                                       0.008242648
## EducationCSEs or equivalent                                                -1.635123160
## EducationNational Vocational Qualification or equivalent                   -1.215969871
## EducationNone of the above                                                 -1.855212427
## EducationO levels/General Certificate of Secondary Education or equivalent -0.674578975
## EducationOther professional qualifications                                 -1.521189444
## Income                                                                      0.225339944
## Average_time_outdoors                                                      -0.238774691
## Summed_PA_min                                                              -0.002410728
## Smoking                                                                    -0.276799925
## Disability                                                                 -0.433555118
## Deprivation_Index                                                          -0.006748655
## Population_density                                                         -0.196455903
##                                                                                   97.5 %
## (Intercept)                                                                21.0384893392
## Natural_environment_300m_10pcnt                                             0.0922313452
## Age                                                                        -2.2337940138
## Sex                                                                         0.0872069241
## BMI                                                                         0.0943511687
## EducationCollege or University Degree                                       0.4916738067
## EducationCSEs or equivalent                                                -0.6317299123
## EducationNational Vocational Qualification or equivalent                   -0.3569086279
## EducationNone of the above                                                 -0.8923018609
## EducationO levels/General Certificate of Secondary Education or equivalent -0.1065824501
## EducationOther professional qualifications                                 -0.6400397747
## Income                                                                      0.3820957202
## Average_time_outdoors                                                      -0.1269383186
## Summed_PA_min                                                              -0.0004841984
## Smoking                                                                    -0.0124759455
## Disability                                                                 -0.0521525133
## Deprivation_Index                                                           0.0043202773
## Population_density                                                          0.1496062014

Model assumption checks

model_diagnostics(lm(Symbol.Digit~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.975, p-value = 0.09067
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  20.592267  
##                                            Natural_environment_300m_10pcnt  
##                                                                   0.048891  
##                                                                        Age  
##                                                                  -2.348265  
##                                                                        Sex  
##                                                                  -0.077582  
##                                                                        BMI  
##                                                                  -0.001522  
##                                      EducationCollege or University Degree  
##                                                                   0.249958  
##                                                EducationCSEs or equivalent  
##                                                                  -1.133427  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  -0.786439  
##                                                 EducationNone of the above  
##                                                                  -1.373757  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  -0.390581  
##                                 EducationOther professional qualifications  
##                                                                  -1.080615  
##                                                                     Income  
##                                                                   0.303718  
##                                                      Average_time_outdoors  
##                                                                  -0.182857  
##                                                              Summed_PA_min  
##                                                                  -0.001447  
##                                                                    Smoking  
##                                                                  -0.144638  
##                                                                 Disability  
##                                                                  -0.242854  
##                                                          Deprivation_Index  
##                                                                  -0.001214  
##                                                         Population_density  
##                                                                  -0.023425  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                        Value p-value                   Decision
## Global Stat        1.449e+04  0.0000 Assumptions NOT satisfied!
## Skewness           2.038e+02  0.0000 Assumptions NOT satisfied!
## Kurtosis           1.428e+04  0.0000 Assumptions NOT satisfied!
## Link Function      1.566e-01  0.6923    Assumptions acceptable.
## Heteroscedasticity 2.701e+00  0.1003    Assumptions acceptable.
  # Residuals vs. Fitted plot 
  # Normal Q-Q plot 
  # Residuals vs. Leverage plot
  # Histogram of residuals
  # Durbin-Watson test 
  # Skewness, Kurtosis, and Heteroskedasticity tests 

6) Regression analyses examining the association of natural environment with brain volumes [cognitive+brain+covariate subset]

6.1) 1000m natural environment buffer

6.1.1) Models for the association of natural environment with grey matter volume

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -170.318, -23.19, 0.448, 24.101, 175.542
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                790.8624
## Natural_environment_1000m_10pcnt                                             0.4641
## Age                                                                        -37.1380
## Sex                                                                         23.9513
## BMI                                                                         -5.1650
## EducationCollege or University Degree                                       -1.6259
## EducationCSEs or equivalent                                                  4.7973
## EducationNational Vocational Qualification or equivalent                     2.6351
## EducationNone of the above                                                   4.3272
## EducationO levels/General Certificate of Secondary Education or equivalent   0.8282
## EducationOther professional qualifications                                   4.1696
## Income                                                                      -0.3610
##                                                                            Std. Error
## (Intercept)                                                                    1.4890
## Natural_environment_1000m_10pcnt                                               0.1495
## Age                                                                            0.4768
## Sex                                                                            0.6854
## BMI                                                                            0.3978
## EducationCollege or University Degree                                          1.0144
## EducationCSEs or equivalent                                                    2.1007
## EducationNational Vocational Qualification or equivalent                       1.8008
## EducationNone of the above                                                     2.0103
## EducationO levels/General Certificate of Secondary Education or equivalent     1.1910
## EducationOther professional qualifications                                     1.8497
## Income                                                                         0.3247
##                                                                            t value
## (Intercept)                                                                531.128
## Natural_environment_1000m_10pcnt                                             3.105
## Age                                                                        -77.891
## Sex                                                                         34.944
## BMI                                                                        -12.983
## EducationCollege or University Degree                                       -1.603
## EducationCSEs or equivalent                                                  2.284
## EducationNational Vocational Qualification or equivalent                     1.463
## EducationNone of the above                                                   2.152
## EducationO levels/General Certificate of Secondary Education or equivalent   0.695
## EducationOther professional qualifications                                   2.254
## Income                                                                      -1.112
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00191
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.10900
## EducationCSEs or equivalent                                                 0.02241
## EducationNational Vocational Qualification or equivalent                    0.14343
## EducationNone of the above                                                  0.03138
## EducationO levels/General Certificate of Secondary Education or equivalent  0.48686
## EducationOther professional qualifications                                  0.02420
## Income                                                                      0.26627
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.49 on 11436 degrees of freedom
## Multiple R-squared:  0.4517, Adjusted R-squared:  0.4512 
## F-statistic: 856.5 on 11 and 11436 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

model6b1 <- lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model6b1)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.628, -22.85, 0.206, 24.084, 178.535
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.025416
## Natural_environment_1000m_10pcnt                                             0.628654
## Age                                                                        -36.894600
## Sex                                                                         23.666981
## BMI                                                                         -4.977473
## EducationCollege or University Degree                                       -1.879776
## EducationCSEs or equivalent                                                  5.135803
## EducationNational Vocational Qualification or equivalent                     2.976558
## EducationNone of the above                                                   4.998400
## EducationO levels/General Certificate of Secondary Education or equivalent   1.003089
## EducationOther professional qualifications                                   4.242883
## Income                                                                      -0.425565
## Average_time_outdoors                                                        0.212077
## Summed_PA_min                                                               -0.004426
## Smoking                                                                     -5.094501
## Disability                                                                  -1.301115
## Deprivation_Index                                                           -0.011229
## Population_density                                                          -1.396443
##                                                                            Std. Error
## (Intercept)                                                                  1.908767
## Natural_environment_1000m_10pcnt                                             0.201496
## Age                                                                          0.479081
## Sex                                                                          0.689788
## BMI                                                                          0.401262
## EducationCollege or University Degree                                        1.012428
## EducationCSEs or equivalent                                                  2.099398
## EducationNational Vocational Qualification or equivalent                     1.797328
## EducationNone of the above                                                   2.014652
## EducationO levels/General Certificate of Secondary Education or equivalent   1.188382
## EducationOther professional qualifications                                   1.843607
## Income                                                                       0.327985
## Average_time_outdoors                                                        0.233931
## Summed_PA_min                                                                0.004031
## Smoking                                                                      0.553626
## Disability                                                                   0.797999
## Deprivation_Index                                                            0.023160
## Population_density                                                           0.735163
##                                                                            t value
## (Intercept)                                                                419.132
## Natural_environment_1000m_10pcnt                                             3.120
## Age                                                                        -77.011
## Sex                                                                         34.310
## BMI                                                                        -12.405
## EducationCollege or University Degree                                       -1.857
## EducationCSEs or equivalent                                                  2.446
## EducationNational Vocational Qualification or equivalent                     1.656
## EducationNone of the above                                                   2.481
## EducationO levels/General Certificate of Secondary Education or equivalent   0.844
## EducationOther professional qualifications                                   2.301
## Income                                                                      -1.298
## Average_time_outdoors                                                        0.907
## Summed_PA_min                                                               -1.098
## Smoking                                                                     -9.202
## Disability                                                                  -1.630
## Deprivation_Index                                                           -0.485
## Population_density                                                          -1.900
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00181
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.06338
## EducationCSEs or equivalent                                                 0.01445
## EducationNational Vocational Qualification or equivalent                    0.09773
## EducationNone of the above                                                  0.01311
## EducationO levels/General Certificate of Secondary Education or equivalent  0.39864
## EducationOther professional qualifications                                  0.02139
## Income                                                                      0.19448
## Average_time_outdoors                                                       0.36465
## Summed_PA_min                                                               0.27223
## Smoking                                                                     < 2e-16
## Disability                                                                  0.10303
## Deprivation_Index                                                           0.62779
## Population_density                                                          0.05752
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                   .  
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                         .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.36 on 11430 degrees of freedom
## Multiple R-squared:  0.4562, Adjusted R-squared:  0.4554 
## F-statistic:   564 on 17 and 11430 DF,  p-value: < 2.2e-16
confint(model6b1,"Natural_environment_1000m_10pcnt") #95% confidence interval
##                                      2.5 %  97.5 %
## Natural_environment_1000m_10pcnt 0.2336873 1.02362

Line graph illustration of the full adjusted model

mdl.5b<-resid(lm(Grey_matter_volume_adjusted_T2_cm3~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

mdl.6b<-resid(lm(Natural_environment_1000m_10pcnt~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

GMV.graph<-as.data.frame(cbind(mdl.5b,mdl.6b))
GMV.graph$mdl.5b<-GMV.graph$mdl.5b + mean(CogsBrainCov.df2$Grey_matter_volume_adjusted_T2_cm3)
GMV.graph$mdl.6b<-GMV.graph$mdl.6b*10 + mean(CogsBrainCov.df2$Natural_environment_1000m_10pcnt)*10


ggplot(data = GMV.graph, aes(x = mdl.6b, y = mdl.5b)) + 
  labs(x="Natural Environment (%)", y="Grey Matter Volume (cm^3)")  + geom_smooth(method= 'lm',  se = TRUE, color= 'black') +
  coord_cartesian(xlim=c(0,100)) +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
                     panel.grid.minor = element_blank(), axis.line = element_line(colour = "black"))
## `geom_smooth()` using formula = 'y ~ x'

Model assumption checks

model_diagnostics(model6b1)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9859, p-value = 0.2251
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                 800.025416  
##                                           Natural_environment_1000m_10pcnt  
##                                                                   0.628654  
##                                                                        Age  
##                                                                 -36.894600  
##                                                                        Sex  
##                                                                  23.666981  
##                                                                        BMI  
##                                                                  -4.977473  
##                                      EducationCollege or University Degree  
##                                                                  -1.879776  
##                                                EducationCSEs or equivalent  
##                                                                   5.135803  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                   2.976558  
##                                                 EducationNone of the above  
##                                                                   4.998400  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                   1.003089  
##                                 EducationOther professional qualifications  
##                                                                   4.242883  
##                                                                     Income  
##                                                                  -0.425565  
##                                                      Average_time_outdoors  
##                                                                   0.212077  
##                                                              Summed_PA_min  
##                                                                  -0.004426  
##                                                                    Smoking  
##                                                                  -5.094501  
##                                                                 Disability  
##                                                                  -1.301115  
##                                                          Deprivation_Index  
##                                                                  -0.011229  
##                                                         Population_density  
##                                                                  -1.396443  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        30.7757 3.401e-06 Assumptions NOT satisfied!
## Skewness           15.2524 9.406e-05 Assumptions NOT satisfied!
## Kurtosis           13.3471 2.588e-04 Assumptions NOT satisfied!
## Link Function       1.4514 2.283e-01    Assumptions acceptable.
## Heteroscedasticity  0.7248 3.946e-01    Assumptions acceptable.

6.1.2) Models for the association of natural environment with white matter volume

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.748, -26.214, -1.057, 24.481, 181.901
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                701.8448
## Natural_environment_1000m_10pcnt                                             0.4815
## Age                                                                        -17.3042
## Sex                                                                         -9.3695
## BMI                                                                          0.3186
## EducationCollege or University Degree                                       -2.5582
## EducationCSEs or equivalent                                                  0.9773
## EducationNational Vocational Qualification or equivalent                    -0.3366
## EducationNone of the above                                                   3.6594
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.7606
## EducationOther professional qualifications                                   1.2015
## Income                                                                      -0.2742
##                                                                            Std. Error
## (Intercept)                                                                    1.6149
## Natural_environment_1000m_10pcnt                                               0.1621
## Age                                                                            0.5171
## Sex                                                                            0.7434
## BMI                                                                            0.4315
## EducationCollege or University Degree                                          1.1002
## EducationCSEs or equivalent                                                    2.2783
## EducationNational Vocational Qualification or equivalent                       1.9531
## EducationNone of the above                                                     2.1803
## EducationO levels/General Certificate of Secondary Education or equivalent     1.2917
## EducationOther professional qualifications                                     2.0061
## Income                                                                         0.3522
##                                                                            t value
## (Intercept)                                                                434.604
## Natural_environment_1000m_10pcnt                                             2.970
## Age                                                                        -33.464
## Sex                                                                        -12.604
## BMI                                                                          0.738
## EducationCollege or University Degree                                       -2.325
## EducationCSEs or equivalent                                                  0.429
## EducationNational Vocational Qualification or equivalent                    -0.172
## EducationNone of the above                                                   1.678
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.589
## EducationOther professional qualifications                                   0.599
## Income                                                                      -0.779
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00298
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.46027
## EducationCollege or University Degree                                       0.02008
## EducationCSEs or equivalent                                                 0.66795
## EducationNational Vocational Qualification or equivalent                    0.86318
## EducationNone of the above                                                  0.09330
## EducationO levels/General Certificate of Secondary Education or equivalent  0.55596
## EducationOther professional qualifications                                  0.54922
## Income                                                                      0.43619
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.49 on 11436 degrees of freedom
## Multiple R-squared:  0.1012, Adjusted R-squared:  0.1004 
## F-statistic: 117.1 on 11 and 11436 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

model6b2 <- lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model6b2)
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.551, -26.148, -1.205, 24.374, 179.13
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                703.760638
## Natural_environment_1000m_10pcnt                                             0.658567
## Age                                                                        -17.223770
## Sex                                                                         -9.422878
## BMI                                                                          0.416262
## EducationCollege or University Degree                                       -2.528885
## EducationCSEs or equivalent                                                  0.918089
## EducationNational Vocational Qualification or equivalent                    -0.396864
## EducationNone of the above                                                   3.604664
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.782634
## EducationOther professional qualifications                                   1.232106
## Income                                                                      -0.257224
## Average_time_outdoors                                                        0.010163
## Summed_PA_min                                                                0.002780
## Smoking                                                                     -0.634877
## Disability                                                                  -1.098450
## Deprivation_Index                                                           -0.036696
## Population_density                                                          -1.059536
##                                                                            Std. Error
## (Intercept)                                                                  2.077939
## Natural_environment_1000m_10pcnt                                             0.219354
## Age                                                                          0.521541
## Sex                                                                          0.750924
## BMI                                                                          0.436826
## EducationCollege or University Degree                                        1.102159
## EducationCSEs or equivalent                                                  2.285465
## EducationNational Vocational Qualification or equivalent                     1.956624
## EducationNone of the above                                                   2.193208
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293707
## EducationOther professional qualifications                                   2.007004
## Income                                                                       0.357053
## Average_time_outdoors                                                        0.254664
## Summed_PA_min                                                                0.004388
## Smoking                                                                      0.602693
## Disability                                                                   0.868725
## Deprivation_Index                                                            0.025213
## Population_density                                                           0.800320
##                                                                            t value
## (Intercept)                                                                338.682
## Natural_environment_1000m_10pcnt                                             3.002
## Age                                                                        -33.025
## Sex                                                                        -12.548
## BMI                                                                          0.953
## EducationCollege or University Degree                                       -2.294
## EducationCSEs or equivalent                                                  0.402
## EducationNational Vocational Qualification or equivalent                    -0.203
## EducationNone of the above                                                   1.644
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.605
## EducationOther professional qualifications                                   0.614
## Income                                                                      -0.720
## Average_time_outdoors                                                        0.040
## Summed_PA_min                                                                0.633
## Smoking                                                                     -1.053
## Disability                                                                  -1.264
## Deprivation_Index                                                           -1.455
## Population_density                                                          -1.324
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00269
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.34065
## EducationCollege or University Degree                                       0.02178
## EducationCSEs or equivalent                                                 0.68791
## EducationNational Vocational Qualification or equivalent                    0.83927
## EducationNone of the above                                                  0.10030
## EducationO levels/General Certificate of Secondary Education or equivalent  0.54522
## EducationOther professional qualifications                                  0.53929
## Income                                                                      0.47129
## Average_time_outdoors                                                       0.96817
## Summed_PA_min                                                               0.52646
## Smoking                                                                     0.29218
## Disability                                                                  0.20610
## Deprivation_Index                                                           0.14557
## Population_density                                                          0.18557
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.49 on 11430 degrees of freedom
## Multiple R-squared:  0.1018, Adjusted R-squared:  0.1004 
## F-statistic: 76.19 on 17 and 11430 DF,  p-value: < 2.2e-16
confint(model6b2,"Natural_environment_1000m_10pcnt") #95% confidence interval
##                                      2.5 %   97.5 %
## Natural_environment_1000m_10pcnt 0.2285958 1.088539

Line graph illustration of the full adjusted model

mdl.7b<-resid(lm(White_matter_volume_adjusted_T2_cm3~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

mdl.8b<-resid(lm(Natural_environment_1000m_10pcnt~Age + Sex + BMI + Education + Income + 
                  Average_time_outdoors + 
                  Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

WMV.graph<-as.data.frame(cbind(mdl.7b,mdl.8b))
WMV.graph$mdl.7b<-WMV.graph$mdl.7b + mean(CogsBrainCov.df2$White_matter_volume_adjusted_T2_cm3)
WMV.graph$mdl.8b<-WMV.graph$mdl.8b*10 + mean(CogsBrainCov.df2$Natural_environment_1000m_10pcnt)*10


ggplot(data = WMV.graph, aes(x = mdl.8b, y = mdl.7b)) + 
  labs(x="Natural Environment (%)", y="White Matter Volume (cm^3)")  + geom_smooth(method= 'lm',  se = TRUE, color= 'black') +
  xlim(0,100) +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
                     panel.grid.minor = element_blank(), axis.line = element_line(colour = "black"))
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 10 rows containing non-finite values (`stat_smooth()`).

Model assumption checks

model_diagnostics(model6b2)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.984, p-value = 0.1965
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  703.76064  
##                                           Natural_environment_1000m_10pcnt  
##                                                                    0.65857  
##                                                                        Age  
##                                                                  -17.22377  
##                                                                        Sex  
##                                                                   -9.42288  
##                                                                        BMI  
##                                                                    0.41626  
##                                      EducationCollege or University Degree  
##                                                                   -2.52889  
##                                                EducationCSEs or equivalent  
##                                                                    0.91809  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                   -0.39686  
##                                                 EducationNone of the above  
##                                                                    3.60466  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                   -0.78263  
##                                 EducationOther professional qualifications  
##                                                                    1.23211  
##                                                                     Income  
##                                                                   -0.25722  
##                                                      Average_time_outdoors  
##                                                                    0.01016  
##                                                              Summed_PA_min  
##                                                                    0.00278  
##                                                                    Smoking  
##                                                                   -0.63488  
##                                                                 Disability  
##                                                                   -1.09845  
##                                                          Deprivation_Index  
##                                                                   -0.03670  
##                                                         Population_density  
##                                                                   -1.05954  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        186.949 0.000e+00 Assumptions NOT satisfied!
## Skewness           102.417 0.000e+00 Assumptions NOT satisfied!
## Kurtosis            63.172 1.887e-15 Assumptions NOT satisfied!
## Link Function       17.711 2.571e-05 Assumptions NOT satisfied!
## Heteroscedasticity   3.649 5.609e-02    Assumptions acceptable.

6.1.3) Models for the association of natural environment with hippocampal volume

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5853, -0.3092, 0.0243, 0.3412, 5.666
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.918e+00
## Natural_environment_1000m_10pcnt                                           -5.327e-04
## Age                                                                        -2.187e-01
## Sex                                                                         2.823e-01
## BMI                                                                        -1.664e-02
## EducationCollege or University Degree                                       2.581e-02
## EducationCSEs or equivalent                                                 5.497e-02
## EducationNational Vocational Qualification or equivalent                    5.706e-02
## EducationNone of the above                                                  5.102e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.594e-02
## EducationOther professional qualifications                                  1.574e-02
## Income                                                                      7.565e-05
##                                                                            Std. Error
## (Intercept)                                                                 2.205e-02
## Natural_environment_1000m_10pcnt                                            2.213e-03
## Age                                                                         7.057e-03
## Sex                                                                         1.015e-02
## BMI                                                                         5.889e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.113e-02
## EducationNational Vocational Qualification or equivalent                    2.666e-02
## EducationNone of the above                                                  2.976e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.763e-02
## EducationOther professional qualifications                                  2.738e-02
## Income                                                                      4.808e-03
##                                                                            t value
## (Intercept)                                                                223.093
## Natural_environment_1000m_10pcnt                                            -0.241
## Age                                                                        -30.989
## Sex                                                                         27.817
## BMI                                                                         -2.825
## EducationCollege or University Degree                                        1.719
## EducationCSEs or equivalent                                                  1.766
## EducationNational Vocational Qualification or equivalent                     2.141
## EducationNone of the above                                                   1.714
## EducationO levels/General Certificate of Secondary Education or equivalent   2.038
## EducationOther professional qualifications                                   0.575
## Income                                                                       0.016
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.80976
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.00473
## EducationCollege or University Degree                                       0.08569
## EducationCSEs or equivalent                                                 0.07744
## EducationNational Vocational Qualification or equivalent                    0.03231
## EducationNone of the above                                                  0.08647
## EducationO levels/General Certificate of Secondary Education or equivalent  0.04155
## EducationOther professional qualifications                                  0.56528
## Income                                                                      0.98745
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ** 
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5253 on 11430 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1636, Adjusted R-squared:  0.1628 
## F-statistic: 203.3 on 11 and 11430 DF,  p-value: < 2.2e-16

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

model6b3 <- lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model6b3)
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6122, -0.3096, 0.0245, 0.3388, 5.6423
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Natural_environment_1000m_10pcnt                                            3.896e-04
## Age                                                                        -2.165e-01
## Sex                                                                         2.795e-01
## BMI                                                                        -1.365e-02
## EducationCollege or University Degree                                       2.424e-02
## EducationCSEs or equivalent                                                 5.568e-02
## EducationNational Vocational Qualification or equivalent                    5.854e-02
## EducationNone of the above                                                  5.395e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.685e-02
## EducationOther professional qualifications                                  1.607e-02
## Income                                                                     -3.824e-04
## Average_time_outdoors                                                       3.398e-05
## Summed_PA_min                                                               6.130e-05
## Smoking                                                                    -3.773e-02
## Disability                                                                 -2.216e-02
## Deprivation_Index                                                           6.731e-05
## Population_density                                                         -9.701e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.834e-02
## Natural_environment_1000m_10pcnt                                            2.991e-03
## Age                                                                         7.111e-03
## Sex                                                                         1.024e-02
## BMI                                                                         5.957e-03
## EducationCollege or University Degree                                       1.503e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.991e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.870e-03
## Average_time_outdoors                                                       3.473e-03
## Summed_PA_min                                                               5.984e-05
## Smoking                                                                     8.219e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.438e-04
## Population_density                                                          1.091e-02
##                                                                            t value
## (Intercept)                                                                175.697
## Natural_environment_1000m_10pcnt                                             0.130
## Age                                                                        -30.442
## Sex                                                                         27.291
## BMI                                                                         -2.291
## EducationCollege or University Degree                                        1.613
## EducationCSEs or equivalent                                                  1.785
## EducationNational Vocational Qualification or equivalent                     2.194
## EducationNone of the above                                                   1.804
## EducationO levels/General Certificate of Secondary Education or equivalent   2.088
## EducationOther professional qualifications                                   0.587
## Income                                                                      -0.079
## Average_time_outdoors                                                        0.010
## Summed_PA_min                                                                1.024
## Smoking                                                                     -4.591
## Disability                                                                  -1.870
## Deprivation_Index                                                            0.196
## Population_density                                                          -0.889
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.8964
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0220
## EducationCollege or University Degree                                        0.1069
## EducationCSEs or equivalent                                                  0.0743
## EducationNational Vocational Qualification or equivalent                     0.0282
## EducationNone of the above                                                   0.0713
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0368
## EducationOther professional qualifications                                   0.5572
## Income                                                                       0.9374
## Average_time_outdoors                                                        0.9922
## Summed_PA_min                                                                0.3057
## Smoking                                                                    4.45e-06
## Disability                                                                   0.0615
## Deprivation_Index                                                            0.8448
## Population_density                                                           0.3741
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11424 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.1643 
## F-statistic: 133.4 on 17 and 11424 DF,  p-value: < 2.2e-16
confint(model6b3,"Natural_environment_1000m_10pcnt") #95% confidence interval
##                                         2.5 %      97.5 %
## Natural_environment_1000m_10pcnt -0.005474223 0.006253357

Model assumption checks

model_diagnostics(model6b3)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.0355, p-value = 0.9711
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  4.979e+00  
##                                           Natural_environment_1000m_10pcnt  
##                                                                  3.896e-04  
##                                                                        Age  
##                                                                 -2.165e-01  
##                                                                        Sex  
##                                                                  2.795e-01  
##                                                                        BMI  
##                                                                 -1.365e-02  
##                                      EducationCollege or University Degree  
##                                                                  2.424e-02  
##                                                EducationCSEs or equivalent  
##                                                                  5.568e-02  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  5.854e-02  
##                                                 EducationNone of the above  
##                                                                  5.395e-02  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  3.685e-02  
##                                 EducationOther professional qualifications  
##                                                                  1.607e-02  
##                                                                     Income  
##                                                                 -3.824e-04  
##                                                      Average_time_outdoors  
##                                                                  3.398e-05  
##                                                              Summed_PA_min  
##                                                                  6.130e-05  
##                                                                    Smoking  
##                                                                 -3.773e-02  
##                                                                 Disability  
##                                                                 -2.216e-02  
##                                                          Deprivation_Index  
##                                                                  6.731e-05  
##                                                         Population_density  
##                                                                 -9.701e-03  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                       Value p-value                   Decision
## Global Stat        4069.302 0.00000 Assumptions NOT satisfied!
## Skewness            153.617 0.00000 Assumptions NOT satisfied!
## Kurtosis           3816.295 0.00000 Assumptions NOT satisfied!
## Link Function        96.461 0.00000 Assumptions NOT satisfied!
## Heteroscedasticity    2.928 0.08703    Assumptions acceptable.

6.2) 300m natural environment buffer

6.2.1) Association of natural environment with grey matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -170.538, -23.2, 0.358, 24.174, 175.844
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                791.4841
## Natural_environment_300m_10pcnt                                              0.4509
## Age                                                                        -37.1365
## Sex                                                                         23.9143
## BMI                                                                         -5.1602
## EducationCollege or University Degree                                       -1.6831
## EducationCSEs or equivalent                                                  4.7873
## EducationNational Vocational Qualification or equivalent                     2.6110
## EducationNone of the above                                                   4.2934
## EducationO levels/General Certificate of Secondary Education or equivalent   0.8169
## EducationOther professional qualifications                                   4.1578
## Income                                                                      -0.3895
##                                                                            Std. Error
## (Intercept)                                                                    1.3962
## Natural_environment_300m_10pcnt                                                0.1367
## Age                                                                            0.4766
## Sex                                                                            0.6853
## BMI                                                                            0.3978
## EducationCollege or University Degree                                          1.0139
## EducationCSEs or equivalent                                                    2.1006
## EducationNational Vocational Qualification or equivalent                       1.8008
## EducationNone of the above                                                     2.0102
## EducationO levels/General Certificate of Secondary Education or equivalent     1.1910
## EducationOther professional qualifications                                     1.8496
## Income                                                                         0.3250
##                                                                            t value
## (Intercept)                                                                566.898
## Natural_environment_300m_10pcnt                                              3.298
## Age                                                                        -77.912
## Sex                                                                         34.894
## BMI                                                                        -12.971
## EducationCollege or University Degree                                       -1.660
## EducationCSEs or equivalent                                                  2.279
## EducationNational Vocational Qualification or equivalent                     1.450
## EducationNone of the above                                                   2.136
## EducationO levels/General Certificate of Secondary Education or equivalent   0.686
## EducationOther professional qualifications                                   2.248
## Income                                                                      -1.198
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.000975
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.096920
## EducationCSEs or equivalent                                                0.022681
## EducationNational Vocational Qualification or equivalent                   0.147096
## EducationNone of the above                                                 0.032716
## EducationO levels/General Certificate of Secondary Education or equivalent 0.492800
## EducationOther professional qualifications                                 0.024604
## Income                                                                     0.230855
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ***
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.49 on 11436 degrees of freedom
## Multiple R-squared:  0.4518, Adjusted R-squared:  0.4513 
## F-statistic: 856.7 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                788.7474049
## Natural_environment_300m_10pcnt                                              0.1829441
## Age                                                                        -38.0708514
## Sex                                                                         22.5709135
## BMI                                                                         -5.9399960
## EducationCollege or University Degree                                       -3.6705015
## EducationCSEs or equivalent                                                  0.6698730
## EducationNational Vocational Qualification or equivalent                    -0.9187698
## EducationNone of the above                                                   0.3530722
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.5176497
## EducationOther professional qualifications                                   0.5321318
## Income                                                                      -1.0265820
##                                                                                 97.5 %
## (Intercept)                                                                794.2208620
## Natural_environment_300m_10pcnt                                              0.7188766
## Age                                                                        -36.2022383
## Sex                                                                         25.2576936
## BMI                                                                         -4.3804299
## EducationCollege or University Degree                                        0.3042227
## EducationCSEs or equivalent                                                  8.9047608
## EducationNational Vocational Qualification or equivalent                     6.1408691
## EducationNone of the above                                                   8.2337300
## EducationO levels/General Certificate of Secondary Education or equivalent   3.1513973
## EducationOther professional qualifications                                   7.7833695
## Income                                                                       0.2476585

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.866, -22.744, 0.316, 24.037, 178.929
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.997655
## Natural_environment_300m_10pcnt                                              0.641913
## Age                                                                        -36.885647
## Sex                                                                         23.610690
## BMI                                                                         -4.970383
## EducationCollege or University Degree                                       -1.956796
## EducationCSEs or equivalent                                                  5.127485
## EducationNational Vocational Qualification or equivalent                     2.943823
## EducationNone of the above                                                   4.958456
## EducationO levels/General Certificate of Secondary Education or equivalent   0.986644
## EducationOther professional qualifications                                   4.226740
## Income                                                                      -0.465277
## Average_time_outdoors                                                        0.200294
## Summed_PA_min                                                               -0.004351
## Smoking                                                                     -5.122386
## Disability                                                                  -1.330463
## Deprivation_Index                                                           -0.010816
## Population_density                                                          -1.543862
##                                                                            Std. Error
## (Intercept)                                                                  1.867036
## Natural_environment_300m_10pcnt                                              0.181341
## Age                                                                          0.478956
## Sex                                                                          0.689492
## BMI                                                                          0.401141
## EducationCollege or University Degree                                        1.011361
## EducationCSEs or equivalent                                                  2.099146
## EducationNational Vocational Qualification or equivalent                     1.797196
## EducationNone of the above                                                   2.014454
## EducationO levels/General Certificate of Secondary Education or equivalent   1.188275
## EducationOther professional qualifications                                   1.843406
## Income                                                                       0.327940
## Average_time_outdoors                                                        0.233967
## Summed_PA_min                                                                0.004030
## Smoking                                                                      0.552978
## Disability                                                                   0.797912
## Deprivation_Index                                                            0.023157
## Population_density                                                           0.723978
##                                                                            t value
## (Intercept)                                                                429.021
## Natural_environment_300m_10pcnt                                              3.540
## Age                                                                        -77.013
## Sex                                                                         34.244
## BMI                                                                        -12.391
## EducationCollege or University Degree                                       -1.935
## EducationCSEs or equivalent                                                  2.443
## EducationNational Vocational Qualification or equivalent                     1.638
## EducationNone of the above                                                   2.461
## EducationO levels/General Certificate of Secondary Education or equivalent   0.830
## EducationOther professional qualifications                                   2.293
## Income                                                                      -1.419
## Average_time_outdoors                                                        0.856
## Summed_PA_min                                                               -1.080
## Smoking                                                                     -9.263
## Disability                                                                  -1.667
## Deprivation_Index                                                           -0.467
## Population_density                                                          -2.132
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.000402
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.053038
## EducationCSEs or equivalent                                                0.014595
## EducationNational Vocational Qualification or equivalent                   0.101447
## EducationNone of the above                                                 0.013853
## EducationO levels/General Certificate of Secondary Education or equivalent 0.406377
## EducationOther professional qualifications                                 0.021872
## Income                                                                     0.155989
## Average_time_outdoors                                                      0.391973
## Summed_PA_min                                                              0.280344
## Smoking                                                                     < 2e-16
## Disability                                                                 0.095456
## Deprivation_Index                                                          0.640455
## Population_density                                                         0.032989
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ***
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11430 degrees of freedom
## Multiple R-squared:  0.4563, Adjusted R-squared:  0.4555 
## F-statistic: 564.3 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                797.33794354
## Natural_environment_300m_10pcnt                                              0.28645337
## Age                                                                        -37.82448336
## Sex                                                                         22.25916829
## BMI                                                                         -5.75668887
## EducationCollege or University Degree                                       -3.93923688
## EducationCSEs or equivalent                                                  1.01279946
## EducationNational Vocational Qualification or equivalent                    -0.57899017
## EducationNone of the above                                                   1.00977997
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.34257941
## EducationOther professional qualifications                                   0.61334731
## Income                                                                      -1.10809623
## Average_time_outdoors                                                       -0.25832174
## Summed_PA_min                                                               -0.01225146
## Smoking                                                                     -6.20631783
## Disability                                                                  -2.89450743
## Deprivation_Index                                                           -0.05620709
## Population_density                                                          -2.96298351
##                                                                                   97.5 %
## (Intercept)                                                                804.657366460
## Natural_environment_300m_10pcnt                                              0.997373549
## Age                                                                        -35.946810725
## Sex                                                                         24.962212248
## BMI                                                                         -4.184077687
## EducationCollege or University Degree                                        0.025643979
## EducationCSEs or equivalent                                                  9.242171134
## EducationNational Vocational Qualification or equivalent                     6.466636534
## EducationNone of the above                                                   8.907131232
## EducationO levels/General Certificate of Secondary Education or equivalent   3.315867843
## EducationOther professional qualifications                                   7.840133158
## Income                                                                       0.177542826
## Average_time_outdoors                                                        0.658908951
## Summed_PA_min                                                                0.003549058
## Smoking                                                                     -4.038453660
## Disability                                                                   0.233581982
## Deprivation_Index                                                            0.034575219
## Population_density                                                          -0.124740699

6.2.2) Association of natural environment with white matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -145.156, -26.231, -1.177, 24.439, 182.876
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                702.7117
## Natural_environment_300m_10pcnt                                              0.4031
## Age                                                                        -17.2899
## Sex                                                                         -9.4064
## BMI                                                                          0.3230
## EducationCollege or University Degree                                       -2.6249
## EducationCSEs or equivalent                                                  0.9683
## EducationNational Vocational Qualification or equivalent                    -0.3546
## EducationNone of the above                                                   3.6240
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.7643
## EducationOther professional qualifications                                   1.2019
## Income                                                                      -0.2957
##                                                                            Std. Error
## (Intercept)                                                                    1.5144
## Natural_environment_300m_10pcnt                                                0.1483
## Age                                                                            0.5170
## Sex                                                                            0.7434
## BMI                                                                            0.4315
## EducationCollege or University Degree                                          1.0997
## EducationCSEs or equivalent                                                    2.2784
## EducationNational Vocational Qualification or equivalent                       1.9532
## EducationNone of the above                                                     2.1804
## EducationO levels/General Certificate of Secondary Education or equivalent     1.2918
## EducationOther professional qualifications                                     2.0062
## Income                                                                         0.3526
##                                                                            t value
## (Intercept)                                                                464.027
## Natural_environment_300m_10pcnt                                              2.719
## Age                                                                        -33.443
## Sex                                                                        -12.654
## BMI                                                                          0.748
## EducationCollege or University Degree                                       -2.387
## EducationCSEs or equivalent                                                  0.425
## EducationNational Vocational Qualification or equivalent                    -0.182
## EducationNone of the above                                                   1.662
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.592
## EducationOther professional qualifications                                   0.599
## Income                                                                      -0.839
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.00657
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.45419
## EducationCollege or University Degree                                       0.01701
## EducationCSEs or equivalent                                                 0.67087
## EducationNational Vocational Qualification or equivalent                    0.85595
## EducationNone of the above                                                  0.09652
## EducationO levels/General Certificate of Secondary Education or equivalent  0.55412
## EducationOther professional qualifications                                  0.54913
## Income                                                                      0.40165
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11436 degrees of freedom
## Multiple R-squared:  0.1011, Adjusted R-squared:  0.1002 
## F-statistic: 116.9 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                699.7432902
## Natural_environment_300m_10pcnt                                              0.1124612
## Age                                                                        -18.3033106
## Sex                                                                        -10.8635229
## BMI                                                                         -0.5228425
## EducationCollege or University Degree                                       -4.7805588
## EducationCSEs or equivalent                                                 -3.4977996
## EducationNational Vocational Qualification or equivalent                    -4.1832645
## EducationNone of the above                                                  -0.6499048
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.2964373
## EducationOther professional qualifications                                  -2.7306798
## Income                                                                      -0.9867529
##                                                                                 97.5 %
## (Intercept)                                                                705.6801661
## Natural_environment_300m_10pcnt                                              0.6937692
## Age                                                                        -16.2764884
## Sex                                                                         -7.9492624
## BMI                                                                          1.1687666
## EducationCollege or University Degree                                       -0.4693083
## EducationCSEs or equivalent                                                  5.4343080
## EducationNational Vocational Qualification or equivalent                     3.4740898
## EducationNone of the above                                                   7.8979813
## EducationO levels/General Certificate of Secondary Education or equivalent   1.7679219
## EducationOther professional qualifications                                   5.1344955
## Income                                                                       0.3953731

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.379, -26.121, -1.189, 24.349, 180.518
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                704.844502
## Natural_environment_300m_10pcnt                                              0.527191
## Age                                                                        -17.209154
## Sex                                                                         -9.481208
## BMI                                                                          0.429525
## EducationCollege or University Degree                                       -2.626369
## EducationCSEs or equivalent                                                  0.914232
## EducationNational Vocational Qualification or equivalent                    -0.410286
## EducationNone of the above                                                   3.574336
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.780159
## EducationOther professional qualifications                                   1.233623
## Income                                                                      -0.294132
## Average_time_outdoors                                                        0.003207
## Summed_PA_min                                                                0.002884
## Smoking                                                                     -0.681158
## Disability                                                                  -1.124946
## Deprivation_Index                                                           -0.036218
## Population_density                                                          -0.832837
##                                                                            Std. Error
## (Intercept)                                                                  2.032926
## Natural_environment_300m_10pcnt                                              0.197454
## Age                                                                          0.521512
## Sex                                                                          0.750754
## BMI                                                                          0.436783
## EducationCollege or University Degree                                        1.101222
## EducationCSEs or equivalent                                                  2.285658
## EducationNational Vocational Qualification or equivalent                     1.956880
## EducationNone of the above                                                   2.193442
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293856
## EducationOther professional qualifications                                   2.007196
## Income                                                                       0.357078
## Average_time_outdoors                                                        0.254755
## Summed_PA_min                                                                0.004388
## Smoking                                                                      0.602111
## Disability                                                                   0.868808
## Deprivation_Index                                                            0.025214
## Population_density                                                           0.788305
##                                                                            t value
## (Intercept)                                                                346.714
## Natural_environment_300m_10pcnt                                              2.670
## Age                                                                        -32.999
## Sex                                                                        -12.629
## BMI                                                                          0.983
## EducationCollege or University Degree                                       -2.385
## EducationCSEs or equivalent                                                  0.400
## EducationNational Vocational Qualification or equivalent                    -0.210
## EducationNone of the above                                                   1.630
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.603
## EducationOther professional qualifications                                   0.615
## Income                                                                      -0.824
## Average_time_outdoors                                                        0.013
## Summed_PA_min                                                                0.657
## Smoking                                                                     -1.131
## Disability                                                                  -1.295
## Deprivation_Index                                                           -1.436
## Population_density                                                          -1.056
##                                                                            Pr(>|t|)
## (Intercept)                                                                  <2e-16
## Natural_environment_300m_10pcnt                                              0.0076
## Age                                                                          <2e-16
## Sex                                                                          <2e-16
## BMI                                                                          0.3254
## EducationCollege or University Degree                                        0.0171
## EducationCSEs or equivalent                                                  0.6892
## EducationNational Vocational Qualification or equivalent                     0.8339
## EducationNone of the above                                                   0.1032
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5465
## EducationOther professional qualifications                                   0.5388
## Income                                                                       0.4101
## Average_time_outdoors                                                        0.9900
## Summed_PA_min                                                                0.5111
## Smoking                                                                      0.2580
## Disability                                                                   0.1954
## Deprivation_Index                                                            0.1509
## Population_density                                                           0.2908
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11430 degrees of freedom
## Multiple R-squared:  0.1016, Adjusted R-squared:  0.1003 
## F-statistic: 76.06 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                700.859619398
## Natural_environment_300m_10pcnt                                              0.140148072
## Age                                                                        -18.231407024
## Sex                                                                        -10.952814669
## BMI                                                                         -0.426645120
## EducationCollege or University Degree                                       -4.784952166
## EducationCSEs or equivalent                                                 -3.566050924
## EducationNational Vocational Qualification or equivalent                    -4.246107547
## EducationNone of the above                                                  -0.725185743
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.316337824
## EducationOther professional qualifications                                  -2.700825555
## Income                                                                      -0.994066799
## Average_time_outdoors                                                       -0.496156834
## Summed_PA_min                                                               -0.005718573
## Smoking                                                                     -1.861398764
## Disability                                                                  -2.827958778
## Deprivation_Index                                                           -0.085642002
## Population_density                                                          -2.378049620
##                                                                                  97.5 %
## (Intercept)                                                                708.82938523
## Natural_environment_300m_10pcnt                                              0.91423470
## Age                                                                        -16.18690005
## Sex                                                                         -8.00960075
## BMI                                                                          1.28569518
## EducationCollege or University Degree                                       -0.46778504
## EducationCSEs or equivalent                                                  5.39451412
## EducationNational Vocational Qualification or equivalent                     3.42553482
## EducationNone of the above                                                   7.87385832
## EducationO levels/General Certificate of Secondary Education or equivalent   1.75602022
## EducationOther professional qualifications                                   5.16807224
## Income                                                                       0.40580343
## Average_time_outdoors                                                        0.50257133
## Summed_PA_min                                                                0.01148585
## Smoking                                                                      0.49908374
## Disability                                                                   0.57806658
## Deprivation_Index                                                            0.01320646
## Population_density                                                           0.71237579

6.2.3) Association of natural environment with hippocampal volume (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5795, -0.3098, 0.0253, 0.3412, 5.6671
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                 4.925960
## Natural_environment_300m_10pcnt                                            -0.002969
## Age                                                                        -0.218217
## Sex                                                                         0.282361
## BMI                                                                        -0.016669
## EducationCollege or University Degree                                       0.025593
## EducationCSEs or equivalent                                                 0.055049
## EducationNational Vocational Qualification or equivalent                    0.057351
## EducationNone of the above                                                  0.051043
## EducationO levels/General Certificate of Secondary Education or equivalent  0.036259
## EducationOther professional qualifications                                  0.016234
## Income                                                                      0.000414
##                                                                            Std. Error
## (Intercept)                                                                  0.020670
## Natural_environment_300m_10pcnt                                              0.002024
## Age                                                                          0.007055
## Sex                                                                          0.010146
## BMI                                                                          0.005889
## EducationCollege or University Degree                                        0.015010
## EducationCSEs or equivalent                                                  0.031125
## EducationNational Vocational Qualification or equivalent                     0.026653
## EducationNone of the above                                                   0.029753
## EducationO levels/General Certificate of Secondary Education or equivalent   0.017631
## EducationOther professional qualifications                                   0.027377
## Income                                                                       0.004812
##                                                                            t value
## (Intercept)                                                                238.316
## Natural_environment_300m_10pcnt                                             -1.467
## Age                                                                        -30.932
## Sex                                                                         27.831
## BMI                                                                         -2.831
## EducationCollege or University Degree                                        1.705
## EducationCSEs or equivalent                                                  1.769
## EducationNational Vocational Qualification or equivalent                     2.152
## EducationNone of the above                                                   1.716
## EducationO levels/General Certificate of Secondary Education or equivalent   2.057
## EducationOther professional qualifications                                   0.593
## Income                                                                       0.086
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.14238
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.00465
## EducationCollege or University Degree                                       0.08821
## EducationCSEs or equivalent                                                 0.07699
## EducationNational Vocational Qualification or equivalent                    0.03144
## EducationNone of the above                                                  0.08627
## EducationO levels/General Certificate of Secondary Education or equivalent  0.03975
## EducationOther professional qualifications                                  0.55320
## Income                                                                      0.93144
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ** 
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5253 on 11430 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1638, Adjusted R-squared:  0.163 
## F-statistic: 203.5 on 11 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                 4.885443256
## Natural_environment_300m_10pcnt                                            -0.006936443
## Age                                                                        -0.232044973
## Sex                                                                         0.262473576
## BMI                                                                        -0.028212230
## EducationCollege or University Degree                                      -0.003828970
## EducationCSEs or equivalent                                                -0.005962656
## EducationNational Vocational Qualification or equivalent                    0.005105895
## EducationNone of the above                                                 -0.007277138
## EducationO levels/General Certificate of Secondary Education or equivalent  0.001698942
## EducationOther professional qualifications                                 -0.037428937
## Income                                                                     -0.009018099
##                                                                                   97.5 %
## (Intercept)                                                                 4.9664762710
## Natural_environment_300m_10pcnt                                             0.0009979185
## Age                                                                        -0.2043884244
## Sex                                                                         0.3022474005
## BMI                                                                        -0.0051258929
## EducationCollege or University Degree                                       0.0550148893
## EducationCSEs or equivalent                                                 0.1160596535
## EducationNational Vocational Qualification or equivalent                    0.1095956268
## EducationNone of the above                                                  0.1093639950
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0708190109
## EducationOther professional qualifications                                  0.0698971286
## Income                                                                      0.0098460817

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5991, -0.3084, 0.0237, 0.339, 5.6486
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.982e+00
## Natural_environment_300m_10pcnt                                            -3.764e-03
## Age                                                                        -2.163e-01
## Sex                                                                         2.795e-01
## BMI                                                                        -1.348e-02
## EducationCollege or University Degree                                       2.371e-02
## EducationCSEs or equivalent                                                 5.584e-02
## EducationNational Vocational Qualification or equivalent                    5.912e-02
## EducationNone of the above                                                  5.426e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.740e-02
## EducationOther professional qualifications                                  1.658e-02
## Income                                                                     -2.716e-04
## Average_time_outdoors                                                       1.800e-04
## Summed_PA_min                                                               6.209e-05
## Smoking                                                                    -3.824e-02
## Disability                                                                 -2.207e-02
## Deprivation_Index                                                           6.865e-05
## Population_density                                                          1.128e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.772e-02
## Natural_environment_300m_10pcnt                                             2.693e-03
## Age                                                                         7.110e-03
## Sex                                                                         1.024e-02
## BMI                                                                         5.956e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.119e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.990e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.869e-03
## Average_time_outdoors                                                       3.473e-03
## Summed_PA_min                                                               5.983e-05
## Smoking                                                                     8.210e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.438e-04
## Population_density                                                          1.075e-02
##                                                                            t value
## (Intercept)                                                                179.709
## Natural_environment_300m_10pcnt                                             -1.398
## Age                                                                        -30.427
## Sex                                                                         27.300
## BMI                                                                         -2.263
## EducationCollege or University Degree                                        1.579
## EducationCSEs or equivalent                                                  1.790
## EducationNational Vocational Qualification or equivalent                     2.216
## EducationNone of the above                                                   1.814
## EducationO levels/General Certificate of Secondary Education or equivalent   2.120
## EducationOther professional qualifications                                   0.606
## Income                                                                      -0.056
## Average_time_outdoors                                                        0.052
## Summed_PA_min                                                                1.038
## Smoking                                                                     -4.658
## Disability                                                                  -1.862
## Deprivation_Index                                                            0.200
## Population_density                                                           0.105
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.1623
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0237
## EducationCollege or University Degree                                        0.1145
## EducationCSEs or equivalent                                                  0.0735
## EducationNational Vocational Qualification or equivalent                     0.0267
## EducationNone of the above                                                   0.0697
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0340
## EducationOther professional qualifications                                   0.5445
## Income                                                                       0.9555
## Average_time_outdoors                                                        0.9587
## Summed_PA_min                                                                0.2994
## Smoking                                                                    3.24e-06
## Disability                                                                   0.0626
## Deprivation_Index                                                            0.8417
## Population_density                                                           0.9164
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11424 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1657, Adjusted R-squared:  0.1645 
## F-statistic: 133.5 on 17 and 11424 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.927525e+00
## Natural_environment_300m_10pcnt                                            -9.043970e-03
## Age                                                                        -2.302702e-01
## Sex                                                                         2.593975e-01
## BMI                                                                        -2.515004e-02
## EducationCollege or University Degree                                      -5.730541e-03
## EducationCSEs or equivalent                                                -5.303798e-03
## EducationNational Vocational Qualification or equivalent                    6.825916e-03
## EducationNone of the above                                                 -4.361357e-03
## EducationO levels/General Certificate of Secondary Education or equivalent  2.818960e-03
## EducationOther professional qualifications                                 -3.705681e-02
## Income                                                                     -9.816070e-03
## Average_time_outdoors                                                      -6.628189e-03
## Summed_PA_min                                                              -5.519224e-05
## Smoking                                                                    -5.432889e-02
## Disability                                                                 -4.529470e-02
## Deprivation_Index                                                          -6.052647e-04
## Population_density                                                         -1.994372e-02
##                                                                                   97.5 %
## (Intercept)                                                                 5.0362045608
## Natural_environment_300m_10pcnt                                             0.0015152103
## Age                                                                        -0.2023972454
## Sex                                                                         0.2995292948
## BMI                                                                        -0.0018016983
## EducationCollege or University Degree                                       0.0531421754
## EducationCSEs or equivalent                                                 0.1169912825
## EducationNational Vocational Qualification or equivalent                    0.1114172943
## EducationNone of the above                                                  0.1128730690
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0719866585
## EducationOther professional qualifications                                  0.0702247239
## Income                                                                      0.0092728984
## Average_time_outdoors                                                       0.0069881155
## Summed_PA_min                                                               0.0001793693
## Smoking                                                                    -0.0221444757
## Disability                                                                  0.0011595122
## Deprivation_Index                                                           0.0007425678
## Population_density                                                          0.0222005704

Model assumption checks

#grey matter
model_diagnostics(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9863, p-value = 0.2322
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                 800.997655  
##                                            Natural_environment_300m_10pcnt  
##                                                                   0.641913  
##                                                                        Age  
##                                                                 -36.885647  
##                                                                        Sex  
##                                                                  23.610690  
##                                                                        BMI  
##                                                                  -4.970383  
##                                      EducationCollege or University Degree  
##                                                                  -1.956796  
##                                                EducationCSEs or equivalent  
##                                                                   5.127485  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                   2.943823  
##                                                 EducationNone of the above  
##                                                                   4.958456  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                   0.986644  
##                                 EducationOther professional qualifications  
##                                                                   4.226740  
##                                                                     Income  
##                                                                  -0.465277  
##                                                      Average_time_outdoors  
##                                                                   0.200294  
##                                                              Summed_PA_min  
##                                                                  -0.004351  
##                                                                    Smoking  
##                                                                  -5.122386  
##                                                                 Disability  
##                                                                  -1.330463  
##                                                          Deprivation_Index  
##                                                                  -0.010816  
##                                                         Population_density  
##                                                                  -1.543862  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        30.4678 3.930e-06 Assumptions NOT satisfied!
## Skewness           14.4105 1.470e-04 Assumptions NOT satisfied!
## Kurtosis           13.9797 1.848e-04 Assumptions NOT satisfied!
## Link Function       1.2945 2.552e-01    Assumptions acceptable.
## Heteroscedasticity  0.7831 3.762e-01    Assumptions acceptable.
#white matter
model_diagnostics(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9842, p-value = 0.1993
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                 704.844502  
##                                            Natural_environment_300m_10pcnt  
##                                                                   0.527191  
##                                                                        Age  
##                                                                 -17.209154  
##                                                                        Sex  
##                                                                  -9.481208  
##                                                                        BMI  
##                                                                   0.429525  
##                                      EducationCollege or University Degree  
##                                                                  -2.626369  
##                                                EducationCSEs or equivalent  
##                                                                   0.914232  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  -0.410286  
##                                                 EducationNone of the above  
##                                                                   3.574336  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  -0.780159  
##                                 EducationOther professional qualifications  
##                                                                   1.233623  
##                                                                     Income  
##                                                                  -0.294132  
##                                                      Average_time_outdoors  
##                                                                   0.003207  
##                                                              Summed_PA_min  
##                                                                   0.002884  
##                                                                    Smoking  
##                                                                  -0.681158  
##                                                                 Disability  
##                                                                  -1.124946  
##                                                          Deprivation_Index  
##                                                                  -0.036218  
##                                                         Population_density  
##                                                                  -0.832837  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        189.044 0.000e+00 Assumptions NOT satisfied!
## Skewness           104.573 0.000e+00 Assumptions NOT satisfied!
## Kurtosis            63.771 1.443e-15 Assumptions NOT satisfied!
## Link Function       17.241 3.292e-05 Assumptions NOT satisfied!
## Heteroscedasticity   3.459 6.290e-02    Assumptions acceptable.
#HPC
model_diagnostics(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.0353, p-value = 0.9704
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  4.982e+00  
##                                            Natural_environment_300m_10pcnt  
##                                                                 -3.764e-03  
##                                                                        Age  
##                                                                 -2.163e-01  
##                                                                        Sex  
##                                                                  2.795e-01  
##                                                                        BMI  
##                                                                 -1.348e-02  
##                                      EducationCollege or University Degree  
##                                                                  2.371e-02  
##                                                EducationCSEs or equivalent  
##                                                                  5.584e-02  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  5.912e-02  
##                                                 EducationNone of the above  
##                                                                  5.426e-02  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  3.740e-02  
##                                 EducationOther professional qualifications  
##                                                                  1.658e-02  
##                                                                     Income  
##                                                                 -2.716e-04  
##                                                      Average_time_outdoors  
##                                                                  1.800e-04  
##                                                              Summed_PA_min  
##                                                                  6.209e-05  
##                                                                    Smoking  
##                                                                 -3.824e-02  
##                                                                 Disability  
##                                                                 -2.207e-02  
##                                                          Deprivation_Index  
##                                                                  6.865e-05  
##                                                         Population_density  
##                                                                  1.128e-03  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                       Value p-value                   Decision
## Global Stat        4064.469  0.0000 Assumptions NOT satisfied!
## Skewness            152.624  0.0000 Assumptions NOT satisfied!
## Kurtosis           3815.380  0.0000 Assumptions NOT satisfied!
## Link Function        93.681  0.0000 Assumptions NOT satisfied!
## Heteroscedasticity    2.784  0.0952    Assumptions acceptable.

7) Moderation by sex for cognitive function [cognitive+brain+covariate subset]

7.1) 1000m natural environment buffer

7.1.1) Trails B-A (not significant)

model7trail <- lm(Trails_B_A~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model7trail)
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.947, -10.193, -2.533, 6.958, 175.573
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.323391
## Natural_environment_1000m_10pcnt                                           -0.199179
## Sex                                                                        -0.418222
## Age                                                                         4.106698
## BMI                                                                         0.186647
## EducationCollege or University Degree                                      -0.520533
## EducationCSEs or equivalent                                                 4.188585
## EducationNational Vocational Qualification or equivalent                    6.839147
## EducationNone of the above                                                  9.842178
## EducationO levels/General Certificate of Secondary Education or equivalent  1.702775
## EducationOther professional qualifications                                  3.543078
## Income                                                                     -0.843554
## Average_time_outdoors                                                       0.304832
## Summed_PA_min                                                               0.003395
## Smoking                                                                     0.641003
## Disability                                                                 -0.065044
## Deprivation_Index                                                          -0.037795
## Population_density                                                          0.314296
## Natural_environment_1000m_10pcnt:Sex                                        0.144118
##                                                                            Std. Error
## (Intercept)                                                                  0.956712
## Natural_environment_1000m_10pcnt                                             0.101015
## Sex                                                                          0.785551
## Age                                                                          0.240131
## BMI                                                                          0.201119
## EducationCollege or University Degree                                        0.507464
## EducationCSEs or equivalent                                                  1.052317
## EducationNational Vocational Qualification or equivalent                     0.900930
## EducationNone of the above                                                   1.009882
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595640
## EducationOther professional qualifications                                   0.924057
## Income                                                                       0.164391
## Average_time_outdoors                                                        0.117278
## Summed_PA_min                                                                0.002021
## Smoking                                                                      0.277486
## Disability                                                                   0.399970
## Deprivation_Index                                                            0.011608
## Population_density                                                           0.368476
## Natural_environment_1000m_10pcnt:Sex                                         0.148847
##                                                                            t value
## (Intercept)                                                                 27.514
## Natural_environment_1000m_10pcnt                                            -1.972
## Sex                                                                         -0.532
## Age                                                                         17.102
## BMI                                                                          0.928
## EducationCollege or University Degree                                       -1.026
## EducationCSEs or equivalent                                                  3.980
## EducationNational Vocational Qualification or equivalent                     7.591
## EducationNone of the above                                                   9.746
## EducationO levels/General Certificate of Secondary Education or equivalent   2.859
## EducationOther professional qualifications                                   3.834
## Income                                                                      -5.131
## Average_time_outdoors                                                        2.599
## Summed_PA_min                                                                1.680
## Smoking                                                                      2.310
## Disability                                                                  -0.163
## Deprivation_Index                                                           -3.256
## Population_density                                                           0.853
## Natural_environment_1000m_10pcnt:Sex                                         0.968
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.048659
## Sex                                                                        0.594464
## Age                                                                         < 2e-16
## BMI                                                                        0.353405
## EducationCollege or University Degree                                      0.305029
## EducationCSEs or equivalent                                                6.92e-05
## EducationNational Vocational Qualification or equivalent                   3.42e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004261
## EducationOther professional qualifications                                 0.000127
## Income                                                                     2.92e-07
## Average_time_outdoors                                                      0.009356
## Summed_PA_min                                                              0.092944
## Smoking                                                                    0.020904
## Disability                                                                 0.870819
## Deprivation_Index                                                          0.001134
## Population_density                                                         0.393698
## Natural_environment_1000m_10pcnt:Sex                                       0.332949
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           *  
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11429 degrees of freedom
## Multiple R-squared:  0.07209,    Adjusted R-squared:  0.07063 
## F-statistic: 49.33 on 18 and 11429 DF,  p-value: < 2.2e-16
confint(model7trail,"Natural_environment_1000m_10pcnt:Sex") #95% confidence interval
##                                           2.5 %    97.5 %
## Natural_environment_1000m_10pcnt:Sex -0.1476466 0.4358827

Model assumption checks

#model_diagnostics(model7tmt)

7.1.2) Symbol Digit Substitution (not significant)

model7sds <- lm(Symbol.Digit~Natural_environment_1000m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model7sds)
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.822, -2.468, 0.289, 2.766, 63.403
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.4031173
## Natural_environment_1000m_10pcnt                                            0.1052277
## Sex                                                                        -0.1868042
## Age                                                                        -2.3515649
## BMI                                                                        -0.0051354
## EducationCollege or University Degree                                       0.2704460
## EducationCSEs or equivalent                                                -1.1320161
## EducationNational Vocational Qualification or equivalent                   -0.7873720
## EducationNone of the above                                                 -1.3741910
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3961848
## EducationOther professional qualifications                                 -1.0861857
## Income                                                                      0.3084956
## Average_time_outdoors                                                      -0.1826282
## Summed_PA_min                                                              -0.0014697
## Smoking                                                                    -0.1330025
## Disability                                                                 -0.2395108
## Deprivation_Index                                                          -0.0013057
## Population_density                                                         -0.1531256
## Natural_environment_1000m_10pcnt:Sex                                        0.0249880
##                                                                            Std. Error
## (Intercept)                                                                 0.2325732
## Natural_environment_1000m_10pcnt                                            0.0245564
## Sex                                                                         0.1909647
## Age                                                                         0.0583749
## BMI                                                                         0.0488914
## EducationCollege or University Degree                                       0.1233626
## EducationCSEs or equivalent                                                 0.2558145
## EducationNational Vocational Qualification or equivalent                    0.2190130
## EducationNone of the above                                                  0.2454988
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1447978
## EducationOther professional qualifications                                  0.2246350
## Income                                                                      0.0399629
## Average_time_outdoors                                                       0.0285099
## Summed_PA_min                                                               0.0004912
## Smoking                                                                     0.0674559
## Disability                                                                  0.0972314
## Deprivation_Index                                                           0.0028219
## Population_density                                                          0.0895752
## Natural_environment_1000m_10pcnt:Sex                                        0.0361841
##                                                                            t value
## (Intercept)                                                                 87.728
## Natural_environment_1000m_10pcnt                                             4.285
## Sex                                                                         -0.978
## Age                                                                        -40.284
## BMI                                                                         -0.105
## EducationCollege or University Degree                                        2.192
## EducationCSEs or equivalent                                                 -4.425
## EducationNational Vocational Qualification or equivalent                    -3.595
## EducationNone of the above                                                  -5.598
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.736
## EducationOther professional qualifications                                  -4.835
## Income                                                                       7.720
## Average_time_outdoors                                                       -6.406
## Summed_PA_min                                                               -2.992
## Smoking                                                                     -1.972
## Disability                                                                  -2.463
## Deprivation_Index                                                           -0.463
## Population_density                                                          -1.709
## Natural_environment_1000m_10pcnt:Sex                                         0.691
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           1.84e-05
## Sex                                                                        0.327990
## Age                                                                         < 2e-16
## BMI                                                                        0.916348
## EducationCollege or University Degree                                      0.028379
## EducationCSEs or equivalent                                                9.73e-06
## EducationNational Vocational Qualification or equivalent                   0.000326
## EducationNone of the above                                                 2.22e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.006226
## EducationOther professional qualifications                                 1.35e-06
## Income                                                                     1.26e-14
## Average_time_outdoors                                                      1.55e-10
## Summed_PA_min                                                              0.002775
## Smoking                                                                    0.048668
## Disability                                                                 0.013781
## Deprivation_Index                                                          0.643593
## Population_density                                                         0.087392
## Natural_environment_1000m_10pcnt:Sex                                       0.489843
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                         .  
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.308 on 11429 degrees of freedom
## Multiple R-squared:  0.1983, Adjusted R-squared:  0.197 
## F-statistic:   157 on 18 and 11429 DF,  p-value: < 2.2e-16
confint(model7sds,"Natural_environment_1000m_10pcnt:Sex") #95% confidence interval
##                                            2.5 %     97.5 %
## Natural_environment_1000m_10pcnt:Sex -0.04593893 0.09591497

Model assumption checks

#model_diagnostics(model7sds)

7.2) 300m nature exposure buffer

7.2.1) Moderation by sex: association of natural environment with TMT (B-A) (*significant)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt * Sex + 
##     Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.563, -10.252, -2.549, 6.932, 175.87
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                25.979201
## Natural_environment_300m_10pcnt                                            -0.125001
## Sex                                                                        -0.786552
## Age                                                                         4.095653
## BMI                                                                         0.183680
## EducationCollege or University Degree                                      -0.485905
## EducationCSEs or equivalent                                                 4.186310
## EducationNational Vocational Qualification or equivalent                    6.849535
## EducationNone of the above                                                  9.841279
## EducationO levels/General Certificate of Secondary Education or equivalent  1.698377
## EducationOther professional qualifications                                  3.520665
## Income                                                                     -0.833488
## Average_time_outdoors                                                       0.310283
## Summed_PA_min                                                               0.003308
## Smoking                                                                     0.654881
## Disability                                                                 -0.056675
## Deprivation_Index                                                          -0.037861
## Population_density                                                          0.154172
## Natural_environment_300m_10pcnt:Sex                                         0.283523
##                                                                            Std. Error
## (Intercept)                                                                  0.935847
## Natural_environment_300m_10pcnt                                              0.090923
## Sex                                                                          0.619035
## Age                                                                          0.240081
## BMI                                                                          0.201074
## EducationCollege or University Degree                                        0.506949
## EducationCSEs or equivalent                                                  1.052201
## EducationNational Vocational Qualification or equivalent                     0.900911
## EducationNone of the above                                                   1.009792
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595620
## EducationOther professional qualifications                                   0.924063
## Income                                                                       0.164379
## Average_time_outdoors                                                        0.117327
## Summed_PA_min                                                                0.002020
## Smoking                                                                      0.277186
## Disability                                                                   0.399953
## Deprivation_Index                                                            0.011607
## Population_density                                                           0.362905
## Natural_environment_300m_10pcnt:Sex                                          0.136264
##                                                                            t value
## (Intercept)                                                                 27.760
## Natural_environment_300m_10pcnt                                             -1.375
## Sex                                                                         -1.271
## Age                                                                         17.059
## BMI                                                                          0.913
## EducationCollege or University Degree                                       -0.958
## EducationCSEs or equivalent                                                  3.979
## EducationNational Vocational Qualification or equivalent                     7.603
## EducationNone of the above                                                   9.746
## EducationO levels/General Certificate of Secondary Education or equivalent   2.851
## EducationOther professional qualifications                                   3.810
## Income                                                                      -5.071
## Average_time_outdoors                                                        2.645
## Summed_PA_min                                                                1.637
## Smoking                                                                      2.363
## Disability                                                                  -0.142
## Deprivation_Index                                                           -3.262
## Population_density                                                           0.425
## Natural_environment_300m_10pcnt:Sex                                          2.081
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.16922
## Sex                                                                         0.20389
## Age                                                                         < 2e-16
## BMI                                                                         0.36100
## EducationCollege or University Degree                                       0.33784
## EducationCSEs or equivalent                                                6.97e-05
## EducationNational Vocational Qualification or equivalent                   3.12e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00436
## EducationOther professional qualifications                                  0.00014
## Income                                                                     4.03e-07
## Average_time_outdoors                                                       0.00819
## Summed_PA_min                                                               0.10163
## Smoking                                                                     0.01816
## Disability                                                                  0.88732
## Deprivation_Index                                                           0.00111
## Population_density                                                          0.67097
## Natural_environment_300m_10pcnt:Sex                                         0.03748
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                                 
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                        *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11429 degrees of freedom
## Multiple R-squared:  0.0722, Adjusted R-squared:  0.07074 
## F-statistic: 49.41 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.1447797775
## Natural_environment_300m_10pcnt                                            -0.3032261089
## Sex                                                                        -1.9999676189
## Age                                                                         3.6250528801
## BMI                                                                        -0.2104588585
## EducationCollege or University Degree                                      -1.4796116165
## EducationCSEs or equivalent                                                 2.1238160655
## EducationNational Vocational Qualification or equivalent                    5.0835953873
## EducationNone of the above                                                  7.8619134777
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5308597553
## EducationOther professional qualifications                                  1.7093441169
## Income                                                                     -1.1557000319
## Average_time_outdoors                                                       0.0803012817
## Summed_PA_min                                                              -0.0006526112
## Smoking                                                                     0.1115487721
## Disability                                                                 -0.8406517644
## Deprivation_Index                                                          -0.0606133275
## Population_density                                                         -0.5571846656
## Natural_environment_300m_10pcnt:Sex                                         0.0164229030
##                                                                                  97.5 %
## (Intercept)                                                                27.813622385
## Natural_environment_300m_10pcnt                                             0.053223621
## Sex                                                                         0.426862735
## Age                                                                         4.566253766
## BMI                                                                         0.577819233
## EducationCollege or University Degree                                       0.507800884
## EducationCSEs or equivalent                                                 6.248804754
## EducationNational Vocational Qualification or equivalent                    8.615474824
## EducationNone of the above                                                 11.820643764
## EducationO levels/General Certificate of Secondary Education or equivalent  2.865895133
## EducationOther professional qualifications                                  5.331986865
## Income                                                                     -0.511276457
## Average_time_outdoors                                                       0.540264319
## Summed_PA_min                                                               0.007267844
## Smoking                                                                     1.198213976
## Disability                                                                  0.727301263
## Deprivation_Index                                                          -0.015108750
## Population_density                                                          0.865529156
## Natural_environment_300m_10pcnt:Sex                                         0.550623071

TMT B-A: Sex-stratified subanalysis

#stratify sample by sex
CogsBrainCov.F <- subset(CogsBrainCov.df2,Sex==0.5)
CogsBrainCov.M <- subset(CogsBrainCov.df2,Sex==-0.5)

#repeat regression within each Sex (ensuring to remove Sex as covariate)
#Males
lmM2 <- lm(Trails_B_A ~ Natural_environment_300m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.M)
summary_confint(lmM2)
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Summed_PA_min + 
##     Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.M)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -100.765, -10.01, -2.395, 7.066, 122.049
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.604009
## Natural_environment_300m_10pcnt                                            -0.318386
## Summed_PA_min                                                               0.002904
## Age                                                                         4.032731
## BMI                                                                         0.932547
## EducationCollege or University Degree                                      -0.210591
## EducationCSEs or equivalent                                                 6.708798
## EducationNational Vocational Qualification or equivalent                    7.545591
## EducationNone of the above                                                 14.240131
## EducationO levels/General Certificate of Secondary Education or equivalent  2.506636
## EducationOther professional qualifications                                  5.385367
## Income                                                                     -1.048052
## Average_time_outdoors                                                       0.307734
## Smoking                                                                     0.452331
## Disability                                                                 -0.158264
## Deprivation_Index                                                          -0.042813
## Population_density                                                          0.471765
##                                                                            Std. Error
## (Intercept)                                                                  1.318664
## Natural_environment_300m_10pcnt                                              0.125076
## Summed_PA_min                                                                0.002746
## Age                                                                          0.323030
## BMI                                                                          0.304325
## EducationCollege or University Degree                                        0.720339
## EducationCSEs or equivalent                                                  1.436915
## EducationNational Vocational Qualification or equivalent                     1.098616
## EducationNone of the above                                                   1.331867
## EducationO levels/General Certificate of Secondary Education or equivalent   0.854075
## EducationOther professional qualifications                                   1.435968
## Income                                                                       0.230480
## Average_time_outdoors                                                        0.147083
## Smoking                                                                      0.369502
## Disability                                                                   0.528191
## Deprivation_Index                                                            0.015960
## Population_density                                                           0.494883
##                                                                            t value
## (Intercept)                                                                 20.175
## Natural_environment_300m_10pcnt                                             -2.546
## Summed_PA_min                                                                1.058
## Age                                                                         12.484
## BMI                                                                          3.064
## EducationCollege or University Degree                                       -0.292
## EducationCSEs or equivalent                                                  4.669
## EducationNational Vocational Qualification or equivalent                     6.868
## EducationNone of the above                                                  10.692
## EducationO levels/General Certificate of Secondary Education or equivalent   2.935
## EducationOther professional qualifications                                   3.750
## Income                                                                      -4.547
## Average_time_outdoors                                                        2.092
## Smoking                                                                      1.224
## Disability                                                                  -0.300
## Deprivation_Index                                                           -2.683
## Population_density                                                           0.953
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.010937
## Summed_PA_min                                                              0.290327
## Age                                                                         < 2e-16
## BMI                                                                        0.002192
## EducationCollege or University Degree                                      0.770030
## EducationCSEs or equivalent                                                3.10e-06
## EducationNational Vocational Qualification or equivalent                   7.20e-12
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.003350
## EducationOther professional qualifications                                 0.000178
## Income                                                                     5.55e-06
## Average_time_outdoors                                                      0.036461
## Smoking                                                                    0.220942
## Disability                                                                 0.764467
## Deprivation_Index                                                          0.007327
## Population_density                                                         0.340486
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                        ** 
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      *  
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.98 on 5647 degrees of freedom
## Multiple R-squared:  0.108,  Adjusted R-squared:  0.1054 
## F-statistic: 42.71 on 16 and 5647 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                24.01892153
## Natural_environment_300m_10pcnt                                            -0.56358177
## Summed_PA_min                                                              -0.00247921
## Age                                                                         3.39946745
## BMI                                                                         0.33595361
## EducationCollege or University Degree                                      -1.62273213
## EducationCSEs or equivalent                                                 3.89189208
## EducationNational Vocational Qualification or equivalent                    5.39188163
## EducationNone of the above                                                 11.62915987
## EducationO levels/General Certificate of Secondary Education or equivalent  0.83232049
## EducationOther professional qualifications                                  2.57031842
## Income                                                                     -1.49988094
## Average_time_outdoors                                                       0.01939503
## Smoking                                                                    -0.27203599
## Disability                                                                 -1.19372179
## Deprivation_Index                                                          -0.07410068
## Population_density                                                         -0.49839625
##                                                                                  97.5 %
## (Intercept)                                                                29.189097310
## Natural_environment_300m_10pcnt                                            -0.073189271
## Summed_PA_min                                                               0.008286794
## Age                                                                         4.665994618
## BMI                                                                         1.529140365
## EducationCollege or University Degree                                       1.201550019
## EducationCSEs or equivalent                                                 9.525704556
## EducationNational Vocational Qualification or equivalent                    9.699300089
## EducationNone of the above                                                 16.851103111
## EducationO levels/General Certificate of Secondary Education or equivalent  4.180952417
## EducationOther professional qualifications                                  8.200414998
## Income                                                                     -0.596223823
## Average_time_outdoors                                                       0.596073794
## Smoking                                                                     1.176697710
## Disability                                                                  0.877192863
## Deprivation_Index                                                          -0.011525929
## Population_density                                                          1.441926030
#Females
lmF2 <- lm(Trails_B_A ~ Natural_environment_300m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.F)
summary_confint(lmF2)
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Summed_PA_min + 
##     Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.F)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.619, -10.417, -2.605, 6.997, 176.702
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                25.731272
## Natural_environment_300m_10pcnt                                             0.064483
## Summed_PA_min                                                               0.003181
## Age                                                                         4.241502
## BMI                                                                        -0.290596
## EducationCollege or University Degree                                      -0.603473
## EducationCSEs or equivalent                                                 1.630462
## EducationNational Vocational Qualification or equivalent                    6.131838
## EducationNone of the above                                                  4.474410
## EducationO levels/General Certificate of Secondary Education or equivalent  1.081170
## EducationOther professional qualifications                                  2.394519
## Income                                                                     -0.685553
## Average_time_outdoors                                                       0.177884
## Smoking                                                                     0.788701
## Disability                                                                 -0.020455
## Deprivation_Index                                                          -0.030232
## Population_density                                                         -0.097027
##                                                                            Std. Error
## (Intercept)                                                                  1.325808
## Natural_environment_300m_10pcnt                                              0.131415
## Summed_PA_min                                                                0.002957
## Age                                                                          0.356154
## BMI                                                                          0.270126
## EducationCollege or University Degree                                        0.713106
## EducationCSEs or equivalent                                                  1.535443
## EducationNational Vocational Qualification or equivalent                     1.605106
## EducationNone of the above                                                   1.538805
## EducationO levels/General Certificate of Secondary Education or equivalent   0.830671
## EducationOther professional qualifications                                   1.221032
## Income                                                                       0.233621
## Average_time_outdoors                                                        0.191032
## Smoking                                                                      0.414213
## Disability                                                                   0.603078
## Deprivation_Index                                                            0.016811
## Population_density                                                           0.529322
##                                                                            t value
## (Intercept)                                                                 19.408
## Natural_environment_300m_10pcnt                                              0.491
## Summed_PA_min                                                                1.076
## Age                                                                         11.909
## BMI                                                                         -1.076
## EducationCollege or University Degree                                       -0.846
## EducationCSEs or equivalent                                                  1.062
## EducationNational Vocational Qualification or equivalent                     3.820
## EducationNone of the above                                                   2.908
## EducationO levels/General Certificate of Secondary Education or equivalent   1.302
## EducationOther professional qualifications                                   1.961
## Income                                                                      -2.934
## Average_time_outdoors                                                        0.931
## Smoking                                                                      1.904
## Disability                                                                  -0.034
## Deprivation_Index                                                           -1.798
## Population_density                                                          -0.183
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.623668
## Summed_PA_min                                                              0.282137
## Age                                                                         < 2e-16
## BMI                                                                        0.282071
## EducationCollege or University Degree                                      0.397442
## EducationCSEs or equivalent                                                0.288333
## EducationNational Vocational Qualification or equivalent                   0.000135
## EducationNone of the above                                                 0.003655
## EducationO levels/General Certificate of Secondary Education or equivalent 0.193118
## EducationOther professional qualifications                                 0.049920
## Income                                                                     0.003354
## Average_time_outdoors                                                      0.351803
## Smoking                                                                    0.056948
## Disability                                                                 0.972944
## Deprivation_Index                                                          0.072173
## Population_density                                                         0.854565
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ** 
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                     ** 
## Average_time_outdoors                                                         
## Smoking                                                                    .  
## Disability                                                                    
## Deprivation_Index                                                          .  
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.37 on 5767 degrees of freedom
## Multiple R-squared:  0.0469, Adjusted R-squared:  0.04425 
## F-statistic: 17.74 on 16 and 5767 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                23.1321899257
## Natural_environment_300m_10pcnt                                            -0.1931387691
## Summed_PA_min                                                              -0.0026163016
## Age                                                                         3.5433061904
## BMI                                                                        -0.8201446508
## EducationCollege or University Degree                                      -2.0014278498
## EducationCSEs or equivalent                                                -1.3795830872
## EducationNational Vocational Qualification or equivalent                    2.9852277079
## EducationNone of the above                                                  1.4577743303
## EducationO levels/General Certificate of Secondary Education or equivalent -0.5472567628
## EducationOther professional qualifications                                  0.0008379507
## Income                                                                     -1.1435373222
## Average_time_outdoors                                                      -0.1966099552
## Smoking                                                                    -0.0233122434
## Disability                                                                 -1.2027132458
## Deprivation_Index                                                          -0.0631883660
## Population_density                                                         -1.1346964556
##                                                                                  97.5 %
## (Intercept)                                                                28.330353901
## Natural_environment_300m_10pcnt                                             0.322105049
## Summed_PA_min                                                               0.008977854
## Age                                                                         4.939697279
## BMI                                                                         0.238952273
## EducationCollege or University Degree                                       0.794481458
## EducationCSEs or equivalent                                                 4.640507470
## EducationNational Vocational Qualification or equivalent                    9.278448987
## EducationNone of the above                                                  7.491045453
## EducationO levels/General Certificate of Secondary Education or equivalent  2.709595841
## EducationOther professional qualifications                                  4.788200615
## Income                                                                     -0.227569199
## Average_time_outdoors                                                       0.552377079
## Smoking                                                                     1.600714936
## Disability                                                                  1.161803538
## Deprivation_Index                                                           0.002723739
## Population_density                                                          0.940641847
#obtain beta coefficient and standard error for males and females
F.beta2 <- summary(lmF2)$coefficients["Natural_environment_300m_10pcnt","Estimate"]
F.se2 <- summary(lmF2)$coefficients["Natural_environment_300m_10pcnt","Std. Error"]

M.beta2 <- summary(lmM2)$coefficients["Natural_environment_300m_10pcnt","Estimate"]
M.se2 <- summary(lmM2)$coefficients["Natural_environment_300m_10pcnt","Std. Error"]

#calculate Z-score
Z.nat.tmt <- (M.beta2 - F.beta2) / sqrt(M.se2^2 + F.se2^2)
p.nat.tmt <- 1 - pnorm(Z.nat.tmt)

#print Z-score and p-value
Z.nat.tmt
## [1] -2.110384
p.nat.tmt
## [1] 0.9825873

Model assumption checks

#model_diagnostics(lm(Trails_B_A~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

7.2.2) Moderation by sex: association of natural environment with Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.747, -2.478, 0.278, 2.778, 63.542
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.5922627
## Natural_environment_300m_10pcnt                                             0.0489153
## Sex                                                                        -0.0718062
## Age                                                                        -2.3482462
## BMI                                                                        -0.0015335
## EducationCollege or University Degree                                       0.2499291
## EducationCSEs or equivalent                                                -1.1334766
## EducationNational Vocational Qualification or equivalent                   -0.7865661
## EducationNone of the above                                                 -1.3736422
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3905766
## EducationOther professional qualifications                                 -1.0804964
## Income                                                                      0.3037162
## Average_time_outdoors                                                      -0.1828957
## Summed_PA_min                                                              -0.0014472
## Smoking                                                                    -0.1446153
## Disability                                                                 -0.2428664
## Deprivation_Index                                                          -0.0012146
## Population_density                                                         -0.0234597
## Natural_environment_300m_10pcnt:Sex                                        -0.0015324
##                                                                            Std. Error
## (Intercept)                                                                 0.2276545
## Natural_environment_300m_10pcnt                                             0.0221180
## Sex                                                                         0.1505867
## Age                                                                         0.0584022
## BMI                                                                         0.0489133
## EducationCollege or University Degree                                       0.1233205
## EducationCSEs or equivalent                                                 0.2559587
## EducationNational Vocational Qualification or equivalent                    0.2191558
## EducationNone of the above                                                  0.2456423
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1448907
## EducationOther professional qualifications                                  0.2247878
## Income                                                                      0.0399870
## Average_time_outdoors                                                       0.0285411
## Summed_PA_min                                                               0.0004915
## Smoking                                                                     0.0674284
## Disability                                                                  0.0972927
## Deprivation_Index                                                           0.0028236
## Population_density                                                          0.0882805
## Natural_environment_300m_10pcnt:Sex                                         0.0331475
##                                                                            t value
## (Intercept)                                                                 90.454
## Natural_environment_300m_10pcnt                                              2.212
## Sex                                                                         -0.477
## Age                                                                        -40.208
## BMI                                                                         -0.031
## EducationCollege or University Degree                                        2.027
## EducationCSEs or equivalent                                                 -4.428
## EducationNational Vocational Qualification or equivalent                    -3.589
## EducationNone of the above                                                  -5.592
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.696
## EducationOther professional qualifications                                  -4.807
## Income                                                                       7.595
## Average_time_outdoors                                                       -6.408
## Summed_PA_min                                                               -2.945
## Smoking                                                                     -2.145
## Disability                                                                  -2.496
## Deprivation_Index                                                           -0.430
## Population_density                                                          -0.266
## Natural_environment_300m_10pcnt:Sex                                         -0.046
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.027017
## Sex                                                                        0.633483
## Age                                                                         < 2e-16
## BMI                                                                        0.974990
## EducationCollege or University Degree                                      0.042720
## EducationCSEs or equivalent                                                9.58e-06
## EducationNational Vocational Qualification or equivalent                   0.000333
## EducationNone of the above                                                 2.30e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.007035
## EducationOther professional qualifications                                 1.55e-06
## Income                                                                     3.31e-14
## Average_time_outdoors                                                      1.53e-10
## Summed_PA_min                                                              0.003240
## Smoking                                                                    0.031996
## Disability                                                                 0.012566
## Deprivation_Index                                                          0.667100
## Population_density                                                         0.790444
## Natural_environment_300m_10pcnt:Sex                                        0.963128
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.311 on 11429 degrees of freedom
## Multiple R-squared:  0.1973, Adjusted R-squared:  0.196 
## F-statistic:   156 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.146020766
## Natural_environment_300m_10pcnt                                             0.005560220
## Sex                                                                        -0.366981988
## Age                                                                        -2.462724586
## BMI                                                                        -0.097411898
## EducationCollege or University Degree                                       0.008199798
## EducationCSEs or equivalent                                                -1.635199581
## EducationNational Vocational Qualification or equivalent                   -1.216149136
## EducationNone of the above                                                 -1.855143160
## EducationO levels/General Certificate of Secondary Education or equivalent -0.674587360
## EducationOther professional qualifications                                 -1.521118957
## Income                                                                      0.225334905
## Average_time_outdoors                                                      -0.238841122
## Summed_PA_min                                                              -0.002410578
## Smoking                                                                    -0.276786517
## Disability                                                                 -0.433576724
## Deprivation_Index                                                          -0.006749279
## Population_density                                                         -0.196504566
## Natural_environment_300m_10pcnt:Sex                                        -0.066507250
##                                                                                   97.5 %
## (Intercept)                                                                21.0385045572
## Natural_environment_300m_10pcnt                                             0.0922702917
## Sex                                                                         0.2233695172
## Age                                                                        -2.2337677661
## BMI                                                                         0.0943448750
## EducationCollege or University Degree                                       0.4916583801
## EducationCSEs or equivalent                                                -0.6317535521
## EducationNational Vocational Qualification or equivalent                   -0.3569830476
## EducationNone of the above                                                 -0.8921412019
## EducationO levels/General Certificate of Secondary Education or equivalent -0.1065659293
## EducationOther professional qualifications                                 -0.6398737579
## Income                                                                      0.3820975837
## Average_time_outdoors                                                      -0.1269503706
## Summed_PA_min                                                              -0.0004838455
## Smoking                                                                    -0.0124440023
## Disability                                                                 -0.0521559842
## Deprivation_Index                                                           0.0043201788
## Population_density                                                          0.1495852393
## Natural_environment_300m_10pcnt:Sex                                         0.0634424483

Model assumption checks

#model_diagnostics(lm(Symbol.Digit~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))

8) Moderation by sex for for brain structure [cognitive+brain+covariate subset]

8.1) 1000m natural environment buffer

8.1.1) Grey Matter (SIGNIFICANT)

model8gm <- lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model8gm)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -171.869, -22.885, 0.231, 23.986, 178.833
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.008817
## Natural_environment_1000m_10pcnt                                             0.637728
## Sex                                                                         26.675783
## Age                                                                        -36.902933
## BMI                                                                         -4.976051
## EducationCollege or University Degree                                       -1.898539
## EducationCSEs or equivalent                                                  5.085414
## EducationNational Vocational Qualification or equivalent                     2.924866
## EducationNone of the above                                                   5.061193
## EducationO levels/General Certificate of Secondary Education or equivalent   1.012607
## EducationOther professional qualifications                                   4.263401
## Income                                                                      -0.425866
## Average_time_outdoors                                                        0.201033
## Summed_PA_min                                                               -0.004440
## Smoking                                                                     -5.095234
## Disability                                                                  -1.304596
## Deprivation_Index                                                           -0.011134
## Population_density                                                          -1.399736
## Natural_environment_1000m_10pcnt:Sex                                        -0.634907
##                                                                            Std. Error
## (Intercept)                                                                  1.908485
## Natural_environment_1000m_10pcnt                                             0.201509
## Sex                                                                          1.567047
## Age                                                                          0.479022
## BMI                                                                          0.401200
## EducationCollege or University Degree                                        1.012308
## EducationCSEs or equivalent                                                  2.099202
## EducationNational Vocational Qualification or equivalent                     1.797210
## EducationNone of the above                                                   2.014551
## EducationO levels/General Certificate of Secondary Education or equivalent   1.188204
## EducationOther professional qualifications                                   1.843344
## Income                                                                       0.327933
## Average_time_outdoors                                                        0.233951
## Summed_PA_min                                                                0.004031
## Smoking                                                                      0.553540
## Disability                                                                   0.797876
## Deprivation_Index                                                            0.023157
## Population_density                                                           0.735050
## Natural_environment_1000m_10pcnt:Sex                                         0.296925
##                                                                            t value
## (Intercept)                                                                419.185
## Natural_environment_1000m_10pcnt                                             3.165
## Sex                                                                         17.023
## Age                                                                        -77.038
## BMI                                                                        -12.403
## EducationCollege or University Degree                                       -1.875
## EducationCSEs or equivalent                                                  2.423
## EducationNational Vocational Qualification or equivalent                     1.627
## EducationNone of the above                                                   2.512
## EducationO levels/General Certificate of Secondary Education or equivalent   0.852
## EducationOther professional qualifications                                   2.313
## Income                                                                      -1.299
## Average_time_outdoors                                                        0.859
## Summed_PA_min                                                               -1.102
## Smoking                                                                     -9.205
## Disability                                                                  -1.635
## Deprivation_Index                                                           -0.481
## Population_density                                                          -1.904
## Natural_environment_1000m_10pcnt:Sex                                        -2.138
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00156
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.06076
## EducationCSEs or equivalent                                                 0.01543
## EducationNational Vocational Qualification or equivalent                    0.10367
## EducationNone of the above                                                  0.01201
## EducationO levels/General Certificate of Secondary Education or equivalent  0.39411
## EducationOther professional qualifications                                  0.02075
## Income                                                                      0.19409
## Average_time_outdoors                                                       0.39020
## Summed_PA_min                                                               0.27065
## Smoking                                                                     < 2e-16
## Disability                                                                  0.10206
## Deprivation_Index                                                           0.63066
## Population_density                                                          0.05690
## Natural_environment_1000m_10pcnt:Sex                                        0.03252
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                         .  
## Natural_environment_1000m_10pcnt:Sex                                       *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11429 degrees of freedom
## Multiple R-squared:  0.4564, Adjusted R-squared:  0.4555 
## F-statistic: 533.1 on 18 and 11429 DF,  p-value: < 2.2e-16
confint(model8gm,"Natural_environment_1000m_10pcnt:Sex") #95% confidence interval
##                                         2.5 %      97.5 %
## Natural_environment_1000m_10pcnt:Sex -1.21693 -0.05288327

Grey Matter Graph (no error bars)

#maybe replace this with lmM (2 chunks below), depending on the purpose of scaling
Males.reg.mean<-lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_pcnt_1000m + Age  + BMI + Education + Income + scale(Average_time_outdoors, TRUE) +
                        scale(Summed_PA_min, TRUE) +  Smoking + Disability + scale(Deprivation_Index, TRUE) + Population_density, CogsBrainCov.M)

Males.b0 <- round(Males.reg.mean$coeff[1], digits = 3)
Males.slope <- round(Males.reg.mean$coeff[2], digits = 3)
Males.ci <- predict(Males.reg.mean, interval = "confidence", level = 0.95)

Females.reg.mean<-lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_pcnt_1000m + Age  + BMI + Education + Income + scale(Average_time_outdoors, TRUE) +
                     scale(Summed_PA_min, TRUE) +  Smoking + Disability + scale(Deprivation_Index, TRUE) + Population_density, CogsBrainCov.F)

Females.b0 <- round(Females.reg.mean$coeff[1], digits = 3)
Females.slope <- round(Females.reg.mean$coeff[2], digits = 3)
Females.ci <- predict(Females.reg.mean, interval = "confidence", level = 0.95)

ggplot() +
  #add data points but make colour white so invisible
  #(deleting the points also prevents regression lines from being visible)
  geom_point(data = CogsBrainCov.df2, aes(x = Natural_environment_pcnt_1000m, y = Grey_matter_volume_adjusted_T2_cm3), shape = 20, size = 0, color = "White") +
  #add regression lines for each sex
  geom_abline(aes(intercept= Males.b0, slope = Males.slope, color= "Males"), size = 1) + 
  geom_abline(aes(intercept = Females.b0, slope = Females.slope, color= "Females"), size = 1) +
  #add confidence intervals around regression lines for each sex
  #geom_ribbon(aes(x = CogsBrainCov.M$Natural_environment_pcnt_1000m, ymin = Males.ci[, "lwr"], ymax = Males.ci[,"upr"]), alpha = 0.3) +
  #geom_ribbon(aes(x = CogsBrainCov.F$Natural_environment_pcnt_1000m, ymin = Females.ci[, "lwr"], ymax = Females.ci[,"upr"]), alpha = 0.3) +
  #set plot labels, aesthetics, and legend
  guides(color = guide_legend((title = "Sex"))) + xlab("Natural Environment (%)") +
  ylab("Grey Matter Volume (cm^3)") + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
                                                    panel.grid.minor = element_blank(), axis.line = element_line(colour = "black")) +
 coord_cartesian(xlim=c(0,100),ylim=c(780,820))
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Alternative Grey Matter Graph: Attempt to add error bands to regression lines

# Ensure Education is a factor
CogsBrainCov.M$Education <- as.factor(CogsBrainCov.M$Education)
CogsBrainCov.F$Education <- as.factor(CogsBrainCov.F$Education)

# Ensure Age and BMI are numeric
CogsBrainCov.M$Age <- as.numeric(CogsBrainCov.M$Age)
CogsBrainCov.M$BMI <- as.numeric(CogsBrainCov.M$BMI)
CogsBrainCov.F$Age <- as.numeric(CogsBrainCov.F$Age)
CogsBrainCov.F$BMI <- as.numeric(CogsBrainCov.F$BMI)

# Fit the linear regression model
Males.reg.mean <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_pcnt_1000m + Age + BMI + Education + Income + scale(Average_time_outdoors) + scale(Summed_PA_min) +  Smoking + Disability + scale(Deprivation_Index) + Population_density, data = CogsBrainCov.M)
Females.reg.mean <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_pcnt_1000m + Age + BMI + Education + Income + scale(Average_time_outdoors) + scale(Summed_PA_min) +  Smoking + Disability + scale(Deprivation_Index) + Population_density, data = CogsBrainCov.F)

# Create new data frame for prediction
new_data_M <- data.frame(
    Natural_environment_pcnt_1000m = c(1:100),
    Age = rep(0, 100),
    BMI = rep(0, 100),
    Education = factor(rep(levels(CogsBrainCov.M$Education)[1], 100), levels = levels(CogsBrainCov.M$Education)),
    Income = rep(mean(CogsBrainCov.M$Income, na.rm = TRUE), 100),
    Average_time_outdoors = rep(mean(CogsBrainCov.M$Average_time_outdoors, na.rm = TRUE), 100),
    Summed_PA_min = rep(mean(CogsBrainCov.M$Summed_PA_min, 100), 100),
    Smoking = rep(mean(CogsBrainCov.M$Smoking, na.rm = TRUE), 100),
    Disability = rep(mean(CogsBrainCov.M$Disability, na.rm = TRUE), 100),
    Deprivation_Index = rep(mean(CogsBrainCov.M$Deprivation_Index, na.rm = TRUE), 100),
    Population_density = rep(mean(CogsBrainCov.M$Population_density, na.rm = TRUE), 100)
)
new_data_F <- data.frame(
    Natural_environment_pcnt_1000m = c(1:100),
    Age = rep(0, 100),
    BMI = rep(0, 100),
    Education = factor(rep(levels(CogsBrainCov.F$Education)[1], 100), levels = levels(CogsBrainCov.F$Education)),
    Income = rep(mean(CogsBrainCov.F$Income, na.rm = TRUE), 100),
    Average_time_outdoors = rep(mean(CogsBrainCov.F$Average_time_outdoors, na.rm = TRUE), 100),
    Summed_PA_min = rep(mean(CogsBrainCov.F$Summed_PA_min, 100), 100),
    Smoking = rep(mean(CogsBrainCov.F$Smoking, na.rm = TRUE), 100),
    Disability = rep(mean(CogsBrainCov.F$Disability, na.rm = TRUE), 100),
    Deprivation_Index = rep(mean(CogsBrainCov.F$Deprivation_Index, na.rm = TRUE), 100),
    Population_density = rep(mean(CogsBrainCov.F$Population_density, na.rm = TRUE), 100)
)

# Ensure that all variables are of the correct type
new_data_M$Age <- as.numeric(new_data_M$Age)
new_data_M$BMI <- as.numeric(new_data_M$BMI)
new_data_F$Age <- as.numeric(new_data_F$Age)
new_data_F$BMI <- as.numeric(new_data_F$BMI)

# Get predictions and confidence intervals
predictions_M <- predict(Males.reg.mean, newdata = new_data_M, interval = "confidence", level = 0.95)
predictions_F <- predict(Females.reg.mean, newdata = new_data_F, interval = "confidence", level = 0.95)

# Combine predictions with new_data
new_data_M <- cbind(new_data_M, predictions_M)
new_data_F <- cbind(new_data_F, predictions_F)

# Plot the data, regression line, and confidence intervals
ggplot() +
    geom_line(data = new_data_M, aes(x = Natural_environment_pcnt_1000m, y = fit, color = "Males")) +
    geom_line(data = new_data_F, aes(x = Natural_environment_pcnt_1000m, y = fit, color = "Females")) +
    geom_ribbon(data = new_data_M, aes(x = Natural_environment_pcnt_1000m, ymin = lwr, ymax = upr), alpha = 0.2, fill = "Green") +
    geom_ribbon(data = new_data_F, aes(x = Natural_environment_pcnt_1000m, ymin = lwr, ymax = upr), alpha = 0.2, fill = "Red") +
    guides(color = guide_legend(title = "Sex")) +
  labs(x = "Natural Environment (%)", y = "Grey Matter Volume (cm^3)", color =  "Sex") + 
    theme_classic() 

Alternative Grey Matter Graph: Partial Regression Plot

#residualize GM volume and natural environment within Males
M.resid.gm <- resid(lm(Grey_matter_volume_adjusted_T2_cm3~Age + BMI + Education + Income +                          Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                         Deprivation_Index + Population_density, CogsBrainCov.M))
M.resid.nat <- resid(lm(Natural_environment_1000m_10pcnt~Age + BMI + Education + Income + 
                  Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                    Deprivation_Index + Population_density, CogsBrainCov.M))

#residualize GM volume and natural environment within Females
F.resid.gm <- resid(lm(Grey_matter_volume_adjusted_T2_cm3~Age + BMI + Education + Income +                          Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                         Deprivation_Index + Population_density, CogsBrainCov.F))
F.resid.nat <- resid(lm(Natural_environment_1000m_10pcnt~Age + BMI + Education + Income + 
                  Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                    Deprivation_Index + Population_density, CogsBrainCov.F))

#make data frame of MALE residuals for natural environment and GM volume
M.resid <- as.data.frame(cbind(M.resid.nat, M.resid.gm))
#do NOT add the brain and natural environment means to their respective residuals

#make data frame of FEMALE residuals for natural environment and GM volume
F.resid <- as.data.frame(cbind(F.resid.nat, F.resid.gm))
# do NOT add the FEMALE brain and cog means to their respective residuals

#Plot the partial regression, including confidence intervals
ggplot() +
  #add regression line for females
  geom_smooth(data = F.resid, aes(x = F.resid.nat*10, y = F.resid.gm, color = "Females"), method = "lm", se = TRUE, fill = "red", alpha = 0.1) +
  #add regression line for males
  geom_smooth(data = M.resid, aes(x = M.resid.nat*10, y = M.resid.gm, color = "Males"), method = "lm", se = TRUE, fill = "green", alpha = 0.1) +
  #set plot labels, aesthetics, and legend
  labs(x = "Natural Environment (%)", y = "Grey Matter Volume (cm^3)", color = "Sex") +
  #remove the fill colour from the legend symbols
  guides(color = guide_legend(override.aes = list(fill = NA))) +
  #xlim(0,100) +
  #ylim(785,795) +
  theme_classic()
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Alternative Grey Matter Graph: Partial Regression Plot #2

#residualize GM volume and natural environment within Males
M.resid.gm <- resid(lm(Grey_matter_volume_adjusted_T2_cm3~Age + BMI + Education + Income +                          Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                         Deprivation_Index + Population_density, CogsBrainCov.M))
M.resid.nat <- resid(lm(Natural_environment_1000m_10pcnt~Age + BMI + Education + Income + 
                  Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                         Deprivation_Index + Population_density, CogsBrainCov.M))

#residualize GM volume and natural environment within Females
F.resid.gm <- resid(lm(Grey_matter_volume_adjusted_T2_cm3~Age + BMI + Education + Income +                          Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                         Deprivation_Index + Population_density, CogsBrainCov.F))
F.resid.nat <- resid(lm(Natural_environment_1000m_10pcnt~Age + BMI + Education + Income + 
                  Average_time_outdoors + Summed_PA_min + Smoking + Disability + 
                    Deprivation_Index + Population_density, CogsBrainCov.F))

#make data frame of MALE residuals for natural environment and GM volume
M.resid <- as.data.frame(cbind(M.resid.nat, M.resid.gm))
#add the MALE brain and natural environment means to their respective residuals
M.resid$M.resid.gm <- M.resid$M.resid.gm + mean(CogsBrainCov.M$Grey_matter_volume_adjusted_T2_cm3)
M.resid$M.resid.nat <- M.resid$M.resid.nat*10 + mean(CogsBrainCov.M$Natural_environment_1000m_10pcnt)*10

#make data frame of FEMALE residuals for natural environment and GM volume
F.resid <- as.data.frame(cbind(F.resid.nat, F.resid.gm))
#add the FEMALE brain and cog means to their respective residuals
F.resid$F.resid.gm <- F.resid$F.resid.gm + mean(CogsBrainCov.F$Grey_matter_volume_adjusted_T2_cm3)
F.resid$F.resid.nat <- F.resid$F.resid.nat*10 + mean(CogsBrainCov.F$Natural_environment_1000m_10pcnt)*10

ggplot() +
  #add data points for females
  #geom_point(data = F.resid, aes(x = F.resid.nat, y = F.resid.gm), shape = 20, size = 0, color = "Red") +
  #add data points for males
  #geom_point(data = M.resid, aes(x = M.resid.nat, y = M.resid.gm), shape = 3, size = 0, color = "Green") +
  #add regression line for females
  geom_smooth(data = F.resid, aes(x = F.resid.nat, y = F.resid.gm, color = "Females"), method = "lm", se = TRUE, fill = "red", alpha = 0.1) +
  #add regression line for males
  geom_smooth(data = M.resid, aes(x = M.resid.nat, y = M.resid.gm, color = "Males"), method = "lm", se = TRUE, fill = "green", alpha = 0.2) +
  #set plot labels, aesthetics, and legend
  labs(x = "Natural Environment (%)", y = "Grey Matter Volume (cm^3)", color = "Sex") +
  #remove the fill colour from the legend symbols
  guides(color = guide_legend(override.aes = list(fill = NA))) +
  coord_cartesian(xlim=c(0,96), ylim=c(765,815)) +
  theme_classic()
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

#What is going wrong with these graphs? Why are the slopes so shallow?
#Based on the sex-stratified models (below), y-intercept should be 786 for Males and 813 for Females. Why the discrepancy????

Grey matter: Sex-stratified subanalysis

#repeat regression within each Sex (ensuring to remove Sex as covariate)
#Males
lmM <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.M)
summary(lmM)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.M)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -168.755, -22.696, -0.151, 23.948, 177.675
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                786.794881
## Natural_environment_1000m_10pcnt                                             0.796763
## Summed_PA_min                                                               -0.004975
## Age                                                                        -34.720335
## BMI                                                                         -8.116266
## EducationCollege or University Degree                                       -2.164050
## EducationCSEs or equivalent                                                  5.035193
## EducationNational Vocational Qualification or equivalent                     0.594626
## EducationNone of the above                                                   5.474121
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.911170
## EducationOther professional qualifications                                   5.578208
## Income                                                                      -0.457423
## Average_time_outdoors                                                        0.538271
## Smoking                                                                     -5.440140
## Disability                                                                  -2.243344
## Deprivation_Index                                                            0.024098
## Population_density                                                          -0.892832
##                                                                            Std. Error
## (Intercept)                                                                  2.795423
## Natural_environment_1000m_10pcnt                                             0.286862
## Summed_PA_min                                                                0.005699
## Age                                                                          0.670723
## BMI                                                                          0.631532
## EducationCollege or University Degree                                        1.496091
## EducationCSEs or equivalent                                                  2.982030
## EducationNational Vocational Qualification or equivalent                     2.279555
## EducationNone of the above                                                   2.764168
## EducationO levels/General Certificate of Secondary Education or equivalent   1.772175
## EducationOther professional qualifications                                   2.980559
## Income                                                                       0.478170
## Average_time_outdoors                                                        0.304882
## Smoking                                                                      0.767217
## Disability                                                                   1.095993
## Deprivation_Index                                                            0.033119
## Population_density                                                           1.036245
##                                                                            t value
## (Intercept)                                                                281.458
## Natural_environment_1000m_10pcnt                                             2.778
## Summed_PA_min                                                               -0.873
## Age                                                                        -51.766
## BMI                                                                        -12.852
## EducationCollege or University Degree                                       -1.446
## EducationCSEs or equivalent                                                  1.689
## EducationNational Vocational Qualification or equivalent                     0.261
## EducationNone of the above                                                   1.980
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.514
## EducationOther professional qualifications                                   1.872
## Income                                                                      -0.957
## Average_time_outdoors                                                        1.766
## Smoking                                                                     -7.091
## Disability                                                                  -2.047
## Deprivation_Index                                                            0.728
## Population_density                                                          -0.862
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.0055
## Summed_PA_min                                                                0.3827
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                        0.1481
## EducationCSEs or equivalent                                                  0.0914
## EducationNational Vocational Qualification or equivalent                     0.7942
## EducationNone of the above                                                   0.0477
## EducationO levels/General Certificate of Secondary Education or equivalent   0.6072
## EducationOther professional qualifications                                   0.0613
## Income                                                                       0.3388
## Average_time_outdoors                                                        0.0775
## Smoking                                                                     1.5e-12
## Disability                                                                   0.0407
## Deprivation_Index                                                            0.4669
## Population_density                                                           0.3889
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 .  
## Income                                                                        
## Average_time_outdoors                                                      .  
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.24 on 5647 degrees of freedom
## Multiple R-squared:  0.3726, Adjusted R-squared:  0.3708 
## F-statistic: 209.6 on 16 and 5647 DF,  p-value: < 2.2e-16
confint(lmM,"Natural_environment_1000m_10pcnt")
##                                     2.5 %   97.5 %
## Natural_environment_1000m_10pcnt 0.234403 1.359124
#Females
lmF <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.F)
summary(lmF)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.F)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -143.773, -22.803, 0.161, 23.945, 115.554
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                813.515902
## Natural_environment_1000m_10pcnt                                             0.443942
## Summed_PA_min                                                               -0.004416
## Age                                                                        -39.333232
## BMI                                                                         -2.760310
## EducationCollege or University Degree                                       -2.043069
## EducationCSEs or equivalent                                                  6.005280
## EducationNational Vocational Qualification or equivalent                     6.698965
## EducationNone of the above                                                   3.503267
## EducationO levels/General Certificate of Secondary Education or equivalent   2.789063
## EducationOther professional qualifications                                   3.892558
## Income                                                                      -0.278452
## Average_time_outdoors                                                       -0.295736
## Smoking                                                                     -4.824904
## Disability                                                                  -0.194376
## Deprivation_Index                                                           -0.045641
## Population_density                                                          -1.811383
##                                                                            Std. Error
## (Intercept)                                                                  2.601179
## Natural_environment_1000m_10pcnt                                             0.281578
## Summed_PA_min                                                                0.005672
## Age                                                                          0.683043
## BMI                                                                          0.518339
## EducationCollege or University Degree                                        1.369284
## EducationCSEs or equivalent                                                  2.945543
## EducationNational Vocational Qualification or equivalent                     3.079034
## EducationNone of the above                                                   2.951975
## EducationO levels/General Certificate of Secondary Education or equivalent   1.593553
## EducationOther professional qualifications                                   2.342130
## Income                                                                       0.448247
## Average_time_outdoors                                                        0.366449
## Smoking                                                                      0.795797
## Disability                                                                   1.156908
## Deprivation_Index                                                            0.032252
## Population_density                                                           1.037429
##                                                                            t value
## (Intercept)                                                                312.749
## Natural_environment_1000m_10pcnt                                             1.577
## Summed_PA_min                                                               -0.779
## Age                                                                        -57.585
## BMI                                                                         -5.325
## EducationCollege or University Degree                                       -1.492
## EducationCSEs or equivalent                                                  2.039
## EducationNational Vocational Qualification or equivalent                     2.176
## EducationNone of the above                                                   1.187
## EducationO levels/General Certificate of Secondary Education or equivalent   1.750
## EducationOther professional qualifications                                   1.662
## Income                                                                      -0.621
## Average_time_outdoors                                                       -0.807
## Smoking                                                                     -6.063
## Disability                                                                  -0.168
## Deprivation_Index                                                           -1.415
## Population_density                                                          -1.746
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.1149
## Summed_PA_min                                                                0.4362
## Age                                                                         < 2e-16
## BMI                                                                        1.05e-07
## EducationCollege or University Degree                                        0.1357
## EducationCSEs or equivalent                                                  0.0415
## EducationNational Vocational Qualification or equivalent                     0.0296
## EducationNone of the above                                                   0.2354
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0801
## EducationOther professional qualifications                                   0.0966
## Income                                                                       0.5345
## Average_time_outdoors                                                        0.4197
## Smoking                                                                    1.42e-09
## Disability                                                                   0.8666
## Deprivation_Index                                                            0.1571
## Population_density                                                           0.0809
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                 .  
## Income                                                                        
## Average_time_outdoors                                                         
## Smoking                                                                    ***
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                         .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.23 on 5767 degrees of freedom
## Multiple R-squared:  0.4003, Adjusted R-squared:  0.3987 
## F-statistic: 240.6 on 16 and 5767 DF,  p-value: < 2.2e-16
confint(lmF,"Natural_environment_1000m_10pcnt")
##                                      2.5 %    97.5 %
## Natural_environment_1000m_10pcnt -0.108056 0.9959406
#obtain beta coefficient and standard error for males and females
F.beta <- summary(lmF)$coefficients["Natural_environment_1000m_10pcnt","Estimate"]
F.se <- summary(lmF)$coefficients["Natural_environment_1000m_10pcnt","Std. Error"]

M.beta <- summary(lmM)$coefficients["Natural_environment_1000m_10pcnt","Estimate"]
M.se <- summary(lmM)$coefficients["Natural_environment_1000m_10pcnt","Std. Error"]

#calculate Z-score
Z.nat.gm <- (M.beta - F.beta) / sqrt(M.se^2 + F.se^2)
p.nat.gm <- 1 - pnorm(Z.nat.gm)

#print Z-score and p-value
Z.nat.gm
## [1] 0.8777402
p.nat.gm
## [1] 0.1900424

8.1.2) White Matter (not significant)

model8wm <- lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model8wm)
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.807, -26.221, -1.206, 24.317, 178.604
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                703.752741
## Natural_environment_1000m_10pcnt                                             0.662884
## Sex                                                                         -7.991529
## Age                                                                        -17.227734
## BMI                                                                          0.416939
## EducationCollege or University Degree                                       -2.537811
## EducationCSEs or equivalent                                                  0.894118
## EducationNational Vocational Qualification or equivalent                    -0.421455
## EducationNone of the above                                                   3.634537
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.778106
## EducationOther professional qualifications                                   1.241866
## Income                                                                      -0.257367
## Average_time_outdoors                                                        0.004909
## Summed_PA_min                                                                0.002773
## Smoking                                                                     -0.635226
## Disability                                                                  -1.100106
## Deprivation_Index                                                           -0.036651
## Population_density                                                          -1.061103
## Natural_environment_1000m_10pcnt:Sex                                        -0.302038
##                                                                            Std. Error
## (Intercept)                                                                  2.077968
## Natural_environment_1000m_10pcnt                                             0.219404
## Sex                                                                          1.706209
## Age                                                                          0.521561
## BMI                                                                          0.436829
## EducationCollege or University Degree                                        1.102206
## EducationCSEs or equivalent                                                  2.285622
## EducationNational Vocational Qualification or equivalent                     1.956811
## EducationNone of the above                                                   2.193454
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293723
## EducationOther professional qualifications                                   2.007042
## Income                                                                       0.357055
## Average_time_outdoors                                                        0.254727
## Summed_PA_min                                                                0.004389
## Smoking                                                                      0.602697
## Disability                                                                   0.868732
## Deprivation_Index                                                            0.025213
## Population_density                                                           0.800326
## Natural_environment_1000m_10pcnt:Sex                                         0.323293
##                                                                            t value
## (Intercept)                                                                338.674
## Natural_environment_1000m_10pcnt                                             3.021
## Sex                                                                         -4.684
## Age                                                                        -33.031
## BMI                                                                          0.954
## EducationCollege or University Degree                                       -2.302
## EducationCSEs or equivalent                                                  0.391
## EducationNational Vocational Qualification or equivalent                    -0.215
## EducationNone of the above                                                   1.657
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.601
## EducationOther professional qualifications                                   0.619
## Income                                                                      -0.721
## Average_time_outdoors                                                        0.019
## Summed_PA_min                                                                0.632
## Smoking                                                                     -1.054
## Disability                                                                  -1.266
## Deprivation_Index                                                           -1.454
## Population_density                                                          -1.326
## Natural_environment_1000m_10pcnt:Sex                                        -0.934
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00252
## Sex                                                                        2.85e-06
## Age                                                                         < 2e-16
## BMI                                                                         0.33987
## EducationCollege or University Degree                                       0.02133
## EducationCSEs or equivalent                                                 0.69566
## EducationNational Vocational Qualification or equivalent                    0.82948
## EducationNone of the above                                                  0.09755
## EducationO levels/General Certificate of Secondary Education or equivalent  0.54755
## EducationOther professional qualifications                                  0.53609
## Income                                                                      0.47104
## Average_time_outdoors                                                       0.98462
## Summed_PA_min                                                               0.52745
## Smoking                                                                     0.29192
## Disability                                                                  0.20542
## Deprivation_Index                                                           0.14608
## Population_density                                                          0.18492
## Natural_environment_1000m_10pcnt:Sex                                        0.35019
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.49 on 11429 degrees of freedom
## Multiple R-squared:  0.1018, Adjusted R-squared:  0.1004 
## F-statistic:    72 on 18 and 11429 DF,  p-value: < 2.2e-16
confint(model8wm,"Natural_environment_1000m_10pcnt:Sex") #95% confidence interval
##                                           2.5 %    97.5 %
## Natural_environment_1000m_10pcnt:Sex -0.9357478 0.3316718

8.1.3) Hippocampal volume (not significant)

model8hpc <- lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2)
summary(model8hpc)
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6095, -0.3094, 0.0239, 0.3383, 5.6443
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Natural_environment_1000m_10pcnt                                            4.143e-04
## Sex                                                                         2.876e-01
## Age                                                                        -2.165e-01
## BMI                                                                        -1.364e-02
## EducationCollege or University Degree                                       2.419e-02
## EducationCSEs or equivalent                                                 5.554e-02
## EducationNational Vocational Qualification or equivalent                    5.840e-02
## EducationNone of the above                                                  5.412e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.687e-02
## EducationOther professional qualifications                                  1.612e-02
## Income                                                                     -3.834e-04
## Average_time_outdoors                                                       3.976e-06
## Summed_PA_min                                                               6.125e-05
## Smoking                                                                    -3.774e-02
## Disability                                                                 -2.217e-02
## Deprivation_Index                                                           6.759e-05
## Population_density                                                         -9.711e-03
## Natural_environment_1000m_10pcnt:Sex                                       -1.721e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.834e-02
## Natural_environment_1000m_10pcnt                                            2.992e-03
## Sex                                                                         2.327e-02
## Age                                                                         7.112e-03
## BMI                                                                         5.958e-03
## EducationCollege or University Degree                                       1.503e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.991e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.870e-03
## Average_time_outdoors                                                       3.474e-03
## Summed_PA_min                                                               5.984e-05
## Smoking                                                                     8.219e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.439e-04
## Population_density                                                          1.091e-02
## Natural_environment_1000m_10pcnt:Sex                                        4.409e-03
##                                                                            t value
## (Intercept)                                                                175.688
## Natural_environment_1000m_10pcnt                                             0.138
## Sex                                                                         12.361
## Age                                                                        -30.443
## BMI                                                                         -2.290
## EducationCollege or University Degree                                        1.609
## EducationCSEs or equivalent                                                  1.780
## EducationNational Vocational Qualification or equivalent                     2.189
## EducationNone of the above                                                   1.809
## EducationO levels/General Certificate of Secondary Education or equivalent   2.090
## EducationOther professional qualifications                                   0.589
## Income                                                                      -0.079
## Average_time_outdoors                                                        0.001
## Summed_PA_min                                                                1.024
## Smoking                                                                     -4.591
## Disability                                                                  -1.870
## Deprivation_Index                                                            0.197
## Population_density                                                          -0.890
## Natural_environment_1000m_10pcnt:Sex                                        -0.390
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.8899
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0221
## EducationCollege or University Degree                                        0.1076
## EducationCSEs or equivalent                                                  0.0751
## EducationNational Vocational Qualification or equivalent                     0.0286
## EducationNone of the above                                                   0.0704
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0367
## EducationOther professional qualifications                                   0.5559
## Income                                                                       0.9373
## Average_time_outdoors                                                        0.9991
## Summed_PA_min                                                                0.3061
## Smoking                                                                    4.45e-06
## Disability                                                                   0.0614
## Deprivation_Index                                                            0.8442
## Population_density                                                           0.3736
## Natural_environment_1000m_10pcnt:Sex                                         0.6963
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5249 on 11423 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.1643 
## F-statistic: 125.9 on 18 and 11423 DF,  p-value: < 2.2e-16
confint(model8hpc,"Natural_environment_1000m_10pcnt:Sex") #95% confidence interval
##                                            2.5 %      97.5 %
## Natural_environment_1000m_10pcnt:Sex -0.01036247 0.006921332

Model assumption checks

model_diagnostics(model8gm)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.9859, p-value = 0.2252
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  800.00882  
##                                           Natural_environment_1000m_10pcnt  
##                                                                    0.63773  
##                                                                        Sex  
##                                                                   26.67578  
##                                                                        Age  
##                                                                  -36.90293  
##                                                                        BMI  
##                                                                   -4.97605  
##                                      EducationCollege or University Degree  
##                                                                   -1.89854  
##                                                EducationCSEs or equivalent  
##                                                                    5.08541  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                    2.92487  
##                                                 EducationNone of the above  
##                                                                    5.06119  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                    1.01261  
##                                 EducationOther professional qualifications  
##                                                                    4.26340  
##                                                                     Income  
##                                                                   -0.42587  
##                                                      Average_time_outdoors  
##                                                                    0.20103  
##                                                              Summed_PA_min  
##                                                                   -0.00444  
##                                                                    Smoking  
##                                                                   -5.09523  
##                                                                 Disability  
##                                                                   -1.30460  
##                                                          Deprivation_Index  
##                                                                   -0.01113  
##                                                         Population_density  
##                                                                   -1.39974  
##                                       Natural_environment_1000m_10pcnt:Sex  
##                                                                   -0.63491  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        31.8377 2.065e-06 Assumptions NOT satisfied!
## Skewness           15.7374 7.277e-05 Assumptions NOT satisfied!
## Kurtosis           13.6786 2.169e-04 Assumptions NOT satisfied!
## Link Function       1.5882 2.076e-01    Assumptions acceptable.
## Heteroscedasticity  0.8336 3.612e-01    Assumptions acceptable.
  # Residuals vs. Fitted plot suggests approximately linear
  # Normal Q-Q plot suggests slight non-normal skew
  # Residuals vs. Leverage plot: no concerning outliers
  # Histogram of residuals: approximately normal
  # Durbin-Watson test near 2 suggests independent residuals
  # Skewness, Kurtosis, and Heteroskedasticity tests suggest non-normal but homoskedastic

model_diagnostics(model8wm)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.984, p-value = 0.1965
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                 703.752741  
##                                           Natural_environment_1000m_10pcnt  
##                                                                   0.662884  
##                                                                        Sex  
##                                                                  -7.991529  
##                                                                        Age  
##                                                                 -17.227734  
##                                                                        BMI  
##                                                                   0.416939  
##                                      EducationCollege or University Degree  
##                                                                  -2.537811  
##                                                EducationCSEs or equivalent  
##                                                                   0.894118  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  -0.421455  
##                                                 EducationNone of the above  
##                                                                   3.634537  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  -0.778106  
##                                 EducationOther professional qualifications  
##                                                                   1.241866  
##                                                                     Income  
##                                                                  -0.257367  
##                                                      Average_time_outdoors  
##                                                                   0.004909  
##                                                              Summed_PA_min  
##                                                                   0.002773  
##                                                                    Smoking  
##                                                                  -0.635226  
##                                                                 Disability  
##                                                                  -1.100106  
##                                                          Deprivation_Index  
##                                                                  -0.036651  
##                                                         Population_density  
##                                                                  -1.061103  
##                                       Natural_environment_1000m_10pcnt:Sex  
##                                                                  -0.302038  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value   p-value                   Decision
## Global Stat        187.638 0.000e+00 Assumptions NOT satisfied!
## Skewness           102.373 0.000e+00 Assumptions NOT satisfied!
## Kurtosis            63.383 1.665e-15 Assumptions NOT satisfied!
## Link Function       18.187 2.002e-05 Assumptions NOT satisfied!
## Heteroscedasticity   3.694 5.459e-02    Assumptions acceptable.
  # Residuals vs. Fitted plot suggests approximately linear, some heteroskedasticity, 1 outlier
  # Normal Q-Q plot suggests non-normal skew
  # Residuals vs. Leverage plot: no concerning outliers
  # Histogram of residuals: approximately normal
  # Durbin-Watson test near 2 suggests independent residuals
  # Skewness, Kurtosis, and Heteroskedasticity tests suggest non-normal but homoskedastic

model_diagnostics(model8hpc, bin_width=0.1)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.0354, p-value = 0.9708
## alternative hypothesis: true autocorrelation is greater than 0
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Coefficients:
##                                                                (Intercept)  
##                                                                  4.979e+00  
##                                           Natural_environment_1000m_10pcnt  
##                                                                  4.143e-04  
##                                                                        Sex  
##                                                                  2.876e-01  
##                                                                        Age  
##                                                                 -2.165e-01  
##                                                                        BMI  
##                                                                 -1.364e-02  
##                                      EducationCollege or University Degree  
##                                                                  2.419e-02  
##                                                EducationCSEs or equivalent  
##                                                                  5.554e-02  
##                   EducationNational Vocational Qualification or equivalent  
##                                                                  5.840e-02  
##                                                 EducationNone of the above  
##                                                                  5.412e-02  
## EducationO levels/General Certificate of Secondary Education or equivalent  
##                                                                  3.687e-02  
##                                 EducationOther professional qualifications  
##                                                                  1.612e-02  
##                                                                     Income  
##                                                                 -3.834e-04  
##                                                      Average_time_outdoors  
##                                                                  3.976e-06  
##                                                              Summed_PA_min  
##                                                                  6.125e-05  
##                                                                    Smoking  
##                                                                 -3.774e-02  
##                                                                 Disability  
##                                                                 -2.217e-02  
##                                                          Deprivation_Index  
##                                                                  6.759e-05  
##                                                         Population_density  
##                                                                 -9.711e-03  
##                                       Natural_environment_1000m_10pcnt:Sex  
##                                                                 -1.721e-03  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                       Value p-value                   Decision
## Global Stat        4072.050 0.00000 Assumptions NOT satisfied!
## Skewness            153.290 0.00000 Assumptions NOT satisfied!
## Kurtosis           3818.234 0.00000 Assumptions NOT satisfied!
## Link Function        97.593 0.00000 Assumptions NOT satisfied!
## Heteroscedasticity    2.932 0.08684    Assumptions acceptable.
  # Residuals vs. Fitted plot suggests approximately linear, some heteroskedasticity, 1 outlier
  # Normal Q-Q plot suggests non-normal kurtosis
  # Residuals vs. Leverage plot: a few outliers
  # Histogram of residuals: approximately normal
  # Durbin-Watson test near 2 suggests independent residuals
  # Skewness, Kurtosis, and Heteroskedasticity tests suggest non-normal but homoskedastic

8.2) 300m natural environment buffer

8.2.1) Moderation by sex: Grey Matter (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.182, -22.764, 0.27, 23.863, 179.4
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.995874
## Natural_environment_300m_10pcnt                                              0.652078
## Sex                                                                         26.001780
## Age                                                                        -36.877968
## BMI                                                                         -4.975261
## EducationCollege or University Degree                                       -1.968859
## EducationCSEs or equivalent                                                  5.106773
## EducationNational Vocational Qualification or equivalent                     2.891311
## EducationNone of the above                                                   5.006050
## EducationO levels/General Certificate of Secondary Education or equivalent   0.988328
## EducationOther professional qualifications                                   4.275696
## Income                                                                      -0.465934
## Average_time_outdoors                                                        0.184048
## Summed_PA_min                                                               -0.004247
## Smoking                                                                     -5.112998
## Disability                                                                  -1.335654
## Deprivation_Index                                                           -0.010966
## Population_density                                                          -1.558275
## Natural_environment_300m_10pcnt:Sex                                         -0.634411
##                                                                            Std. Error
## (Intercept)                                                                  1.866673
## Natural_environment_300m_10pcnt                                              0.181358
## Sex                                                                          1.234749
## Age                                                                          0.478874
## BMI                                                                          0.401069
## EducationCollege or University Degree                                        1.011177
## EducationCSEs or equivalent                                                  2.098756
## EducationNational Vocational Qualification or equivalent                     1.796988
## EducationNone of the above                                                   2.014165
## EducationO levels/General Certificate of Secondary Education or equivalent   1.188044
## EducationOther professional qualifications                                   1.843167
## Income                                                                       0.327877
## Average_time_outdoors                                                        0.234025
## Summed_PA_min                                                                0.004030
## Smoking                                                                      0.552885
## Disability                                                                   0.797760
## Deprivation_Index                                                            0.023152
## Population_density                                                           0.723864
## Natural_environment_300m_10pcnt:Sex                                          0.271796
##                                                                            t value
## (Intercept)                                                                429.103
## Natural_environment_300m_10pcnt                                              3.596
## Sex                                                                         21.058
## Age                                                                        -77.010
## BMI                                                                        -12.405
## EducationCollege or University Degree                                       -1.947
## EducationCSEs or equivalent                                                  2.433
## EducationNational Vocational Qualification or equivalent                     1.609
## EducationNone of the above                                                   2.485
## EducationO levels/General Certificate of Secondary Education or equivalent   0.832
## EducationOther professional qualifications                                   2.320
## Income                                                                      -1.421
## Average_time_outdoors                                                        0.786
## Summed_PA_min                                                               -1.054
## Smoking                                                                     -9.248
## Disability                                                                  -1.674
## Deprivation_Index                                                           -0.474
## Population_density                                                          -2.153
## Natural_environment_300m_10pcnt:Sex                                         -2.334
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.000325
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.051548
## EducationCSEs or equivalent                                                0.014980
## EducationNational Vocational Qualification or equivalent                   0.107649
## EducationNone of the above                                                 0.012954
## EducationO levels/General Certificate of Secondary Education or equivalent 0.405486
## EducationOther professional qualifications                                 0.020372
## Income                                                                     0.155325
## Average_time_outdoors                                                      0.431623
## Summed_PA_min                                                              0.291958
## Smoking                                                                     < 2e-16
## Disability                                                                 0.094108
## Deprivation_Index                                                          0.635776
## Population_density                                                         0.031362
## Natural_environment_300m_10pcnt:Sex                                        0.019606
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ***
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         *  
## Natural_environment_300m_10pcnt:Sex                                        *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11429 degrees of freedom
## Multiple R-squared:  0.4566, Adjusted R-squared:  0.4557 
## F-statistic: 533.4 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                797.33687375
## Natural_environment_300m_10pcnt                                              0.29658489
## Sex                                                                         23.58146014
## Age                                                                        -37.81664401
## BMI                                                                         -5.76142390
## EducationCollege or University Degree                                       -3.95094016
## EducationCSEs or equivalent                                                  0.99285075
## EducationNational Vocational Qualification or equivalent                    -0.63109329
## EducationNone of the above                                                   1.05794008
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.34044254
## EducationOther professional qualifications                                   0.66277215
## Income                                                                      -1.10862871
## Average_time_outdoors                                                       -0.27468124
## Summed_PA_min                                                               -0.01214621
## Smoking                                                                     -6.19674803
## Disability                                                                  -2.89940021
## Deprivation_Index                                                           -0.05634803
## Population_density                                                          -2.97717156
## Natural_environment_300m_10pcnt:Sex                                         -1.16717761
##                                                                                   97.5 %
## (Intercept)                                                                804.654873520
## Natural_environment_300m_10pcnt                                              1.007571790
## Sex                                                                         28.422099508
## Age                                                                        -35.939292324
## BMI                                                                         -4.189097280
## EducationCollege or University Degree                                        0.013221237
## EducationCSEs or equivalent                                                  9.220695199
## EducationNational Vocational Qualification or equivalent                     6.413715026
## EducationNone of the above                                                   8.954159796
## EducationO levels/General Certificate of Secondary Education or equivalent   3.317099405
## EducationOther professional qualifications                                   7.888620090
## Income                                                                       0.176760739
## Average_time_outdoors                                                        0.642776867
## Summed_PA_min                                                                0.003652204
## Smoking                                                                     -4.029248203
## Disability                                                                   0.228092878
## Deprivation_Index                                                            0.034416966
## Population_density                                                          -0.139377593
## Natural_environment_300m_10pcnt:Sex                                         -0.101643567

Grey matter: Sex-stratified subanalysis

#repeat regression within each Sex (ensuring to remove Sex as covariate)
#Males
lmM <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.M)
summary(lmM)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.M)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -168.877, -22.532, 0.101, 24.065, 178.159
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                788.027756
## Natural_environment_300m_10pcnt                                              0.882478
## Summed_PA_min                                                               -0.004577
## Age                                                                        -34.668892
## BMI                                                                         -8.122995
## EducationCollege or University Degree                                       -2.236983
## EducationCSEs or equivalent                                                  5.092041
## EducationNational Vocational Qualification or equivalent                     0.524662
## EducationNone of the above                                                   5.376730
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.959401
## EducationOther professional qualifications                                   5.641021
## Income                                                                      -0.515298
## Average_time_outdoors                                                        0.506269
## Smoking                                                                     -5.442359
## Disability                                                                  -2.288083
## Deprivation_Index                                                            0.024123
## Population_density                                                          -1.275243
##                                                                            Std. Error
## (Intercept)                                                                  2.735478
## Natural_environment_300m_10pcnt                                              0.259461
## Summed_PA_min                                                                0.005696
## Age                                                                          0.670104
## BMI                                                                          0.631301
## EducationCollege or University Degree                                        1.494294
## EducationCSEs or equivalent                                                  2.980783
## EducationNational Vocational Qualification or equivalent                     2.279004
## EducationNone of the above                                                   2.762868
## EducationO levels/General Certificate of Secondary Education or equivalent   1.771721
## EducationOther professional qualifications                                   2.978817
## Income                                                                       0.478114
## Average_time_outdoors                                                        0.305114
## Smoking                                                                      0.766508
## Disability                                                                   1.095696
## Deprivation_Index                                                            0.033108
## Population_density                                                           1.026601
##                                                                            t value
## (Intercept)                                                                288.077
## Natural_environment_300m_10pcnt                                              3.401
## Summed_PA_min                                                               -0.804
## Age                                                                        -51.737
## BMI                                                                        -12.867
## EducationCollege or University Degree                                       -1.497
## EducationCSEs or equivalent                                                  1.708
## EducationNational Vocational Qualification or equivalent                     0.230
## EducationNone of the above                                                   1.946
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.542
## EducationOther professional qualifications                                   1.894
## Income                                                                      -1.078
## Average_time_outdoors                                                        1.659
## Smoking                                                                     -7.100
## Disability                                                                  -2.088
## Deprivation_Index                                                            0.729
## Population_density                                                          -1.242
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.000676
## Summed_PA_min                                                              0.421666
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.134445
## EducationCSEs or equivalent                                                0.087638
## EducationNational Vocational Qualification or equivalent                   0.817933
## EducationNone of the above                                                 0.051696
## EducationO levels/General Certificate of Secondary Education or equivalent 0.588179
## EducationOther professional qualifications                                 0.058314
## Income                                                                     0.281181
## Average_time_outdoors                                                      0.097115
## Smoking                                                                     1.4e-12
## Disability                                                                 0.036820
## Deprivation_Index                                                          0.466260
## Population_density                                                         0.214215
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ***
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 .  
## Income                                                                        
## Average_time_outdoors                                                      .  
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.23 on 5647 degrees of freedom
## Multiple R-squared:  0.373,  Adjusted R-squared:  0.3712 
## F-statistic:   210 on 16 and 5647 DF,  p-value: < 2.2e-16
confint(lmM,"Natural_environment_300m_10pcnt")
##                                     2.5 %   97.5 %
## Natural_environment_300m_10pcnt 0.3738349 1.391121
#Females
lmF <- lm(Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.F)
summary(lmF)
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Summed_PA_min + Age + BMI + Education + Income + Average_time_outdoors + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.F)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -144.443, -22.935, 0.131, 24.033, 115.105
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                814.187360
## Natural_environment_300m_10pcnt                                              0.447211
## Summed_PA_min                                                               -0.004525
## Age                                                                        -39.351802
## BMI                                                                         -2.749615
## EducationCollege or University Degree                                       -2.108255
## EducationCSEs or equivalent                                                  5.962541
## EducationNational Vocational Qualification or equivalent                     6.696002
## EducationNone of the above                                                   3.503859
## EducationO levels/General Certificate of Secondary Education or equivalent   2.787987
## EducationOther professional qualifications                                   3.849269
## Income                                                                      -0.304041
## Average_time_outdoors                                                       -0.295263
## Smoking                                                                     -4.861236
## Disability                                                                  -0.212458
## Deprivation_Index                                                           -0.045055
## Population_density                                                          -1.890518
##                                                                            Std. Error
## (Intercept)                                                                  2.543111
## Natural_environment_300m_10pcnt                                              0.252074
## Summed_PA_min                                                                0.005672
## Age                                                                          0.683160
## BMI                                                                          0.518145
## EducationCollege or University Degree                                        1.367850
## EducationCSEs or equivalent                                                  2.945224
## EducationNational Vocational Qualification or equivalent                     3.078849
## EducationNone of the above                                                   2.951673
## EducationO levels/General Certificate of Secondary Education or equivalent   1.593358
## EducationOther professional qualifications                                   2.342134
## Income                                                                       0.448121
## Average_time_outdoors                                                        0.366429
## Smoking                                                                      0.794527
## Disability                                                                   1.156799
## Deprivation_Index                                                            0.032246
## Population_density                                                           1.015323
##                                                                            t value
## (Intercept)                                                                320.154
## Natural_environment_300m_10pcnt                                              1.774
## Summed_PA_min                                                               -0.798
## Age                                                                        -57.603
## BMI                                                                         -5.307
## EducationCollege or University Degree                                       -1.541
## EducationCSEs or equivalent                                                  2.024
## EducationNational Vocational Qualification or equivalent                     2.175
## EducationNone of the above                                                   1.187
## EducationO levels/General Certificate of Secondary Education or equivalent   1.750
## EducationOther professional qualifications                                   1.643
## Income                                                                      -0.678
## Average_time_outdoors                                                       -0.806
## Smoking                                                                     -6.118
## Disability                                                                  -0.184
## Deprivation_Index                                                           -1.397
## Population_density                                                          -1.862
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.0761
## Summed_PA_min                                                                0.4250
## Age                                                                         < 2e-16
## BMI                                                                        1.16e-07
## EducationCollege or University Degree                                        0.1233
## EducationCSEs or equivalent                                                  0.0430
## EducationNational Vocational Qualification or equivalent                     0.0297
## EducationNone of the above                                                   0.2352
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0802
## EducationOther professional qualifications                                   0.1003
## Income                                                                       0.4975
## Average_time_outdoors                                                        0.4204
## Smoking                                                                    1.01e-09
## Disability                                                                   0.8543
## Deprivation_Index                                                            0.1624
## Population_density                                                           0.0627
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            .  
## Summed_PA_min                                                                 
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Smoking                                                                    ***
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                         .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.23 on 5767 degrees of freedom
## Multiple R-squared:  0.4004, Adjusted R-squared:  0.3987 
## F-statistic: 240.7 on 16 and 5767 DF,  p-value: < 2.2e-16
confint(lmF,"Natural_environment_300m_10pcnt")
##                                       2.5 %    97.5 %
## Natural_environment_300m_10pcnt -0.04694904 0.9413705
#obtain beta coefficient and standard error for males and females
F.beta <- summary(lmF)$coefficients["Natural_environment_300m_10pcnt","Estimate"]
F.se <- summary(lmF)$coefficients["Natural_environment_300m_10pcnt","Std. Error"]

M.beta <- summary(lmM)$coefficients["Natural_environment_300m_10pcnt","Estimate"]
M.se <- summary(lmM)$coefficients["Natural_environment_300m_10pcnt","Std. Error"]

#calculate Z-score
Z.nat.gm <- (M.beta - F.beta) / sqrt(M.se^2 + F.se^2)
p.nat.gm <- 1 - pnorm(Z.nat.gm)

#print Z-score and p-value
Z.nat.gm
## [1] 1.203235
p.nat.gm
## [1] 0.1144428

8.2.2) Moderation by sex: White Matter (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.098, -26.112, -1.191, 24.342, 180.283
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                704.843684
## Natural_environment_300m_10pcnt                                              0.531860
## Sex                                                                         -8.382901
## Age                                                                        -17.205626
## BMI                                                                          0.427285
## EducationCollege or University Degree                                       -2.631910
## EducationCSEs or equivalent                                                  0.904718
## EducationNational Vocational Qualification or equivalent                    -0.434407
## EducationNone of the above                                                   3.596198
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.779385
## EducationOther professional qualifications                                   1.256110
## Income                                                                      -0.294434
## Average_time_outdoors                                                       -0.004255
## Summed_PA_min                                                                0.002931
## Smoking                                                                     -0.676845
## Disability                                                                  -1.127330
## Deprivation_Index                                                           -0.036286
## Population_density                                                          -0.839457
## Natural_environment_300m_10pcnt:Sex                                         -0.291406
##                                                                            Std. Error
## (Intercept)                                                                  2.032929
## Natural_environment_300m_10pcnt                                              0.197511
## Sex                                                                          1.344722
## Age                                                                          0.521525
## BMI                                                                          0.436790
## EducationCollege or University Degree                                        1.101238
## EducationCSEs or equivalent                                                  2.285682
## EducationNational Vocational Qualification or equivalent                     1.957036
## EducationNone of the above                                                   2.193557
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293858
## EducationOther professional qualifications                                   2.007329
## Income                                                                       0.357079
## Average_time_outdoors                                                        0.254868
## Summed_PA_min                                                                0.004389
## Smoking                                                                      0.602128
## Disability                                                                   0.868813
## Deprivation_Index                                                            0.025214
## Population_density                                                           0.788335
## Natural_environment_300m_10pcnt:Sex                                          0.296004
##                                                                            t value
## (Intercept)                                                                346.713
## Natural_environment_300m_10pcnt                                              2.693
## Sex                                                                         -6.234
## Age                                                                        -32.991
## BMI                                                                          0.978
## EducationCollege or University Degree                                       -2.390
## EducationCSEs or equivalent                                                  0.396
## EducationNational Vocational Qualification or equivalent                    -0.222
## EducationNone of the above                                                   1.639
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.602
## EducationOther professional qualifications                                   0.626
## Income                                                                      -0.825
## Average_time_outdoors                                                       -0.017
## Summed_PA_min                                                                0.668
## Smoking                                                                     -1.124
## Disability                                                                  -1.298
## Deprivation_Index                                                           -1.439
## Population_density                                                          -1.065
## Natural_environment_300m_10pcnt:Sex                                         -0.984
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.0071
## Sex                                                                        4.71e-10
## Age                                                                         < 2e-16
## BMI                                                                          0.3280
## EducationCollege or University Degree                                        0.0169
## EducationCSEs or equivalent                                                  0.6922
## EducationNational Vocational Qualification or equivalent                     0.8243
## EducationNone of the above                                                   0.1011
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5469
## EducationOther professional qualifications                                   0.5315
## Income                                                                       0.4096
## Average_time_outdoors                                                        0.9867
## Summed_PA_min                                                                0.5042
## Smoking                                                                      0.2610
## Disability                                                                   0.1945
## Deprivation_Index                                                            0.1501
## Population_density                                                           0.2870
## Natural_environment_300m_10pcnt:Sex                                          0.3249
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11429 degrees of freedom
## Multiple R-squared:  0.1017, Adjusted R-squared:  0.1003 
## F-statistic: 71.89 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                700.858795415
## Natural_environment_300m_10pcnt                                              0.144704981
## Sex                                                                        -11.018786296
## Age                                                                        -18.227905374
## BMI                                                                         -0.428898213
## EducationCollege or University Degree                                       -4.790524230
## EducationCSEs or equivalent                                                 -3.575610910
## EducationNational Vocational Qualification or equivalent                    -4.270534052
## EducationNone of the above                                                  -0.703550258
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.315568121
## EducationOther professional qualifications                                  -2.678598588
## Income                                                                      -0.994369919
## Average_time_outdoors                                                       -0.503840739
## Summed_PA_min                                                               -0.005671251
## Smoking                                                                     -1.857119545
## Disability                                                                  -2.830352080
## Deprivation_Index                                                           -0.085710974
## Population_density                                                          -2.384728065
## Natural_environment_300m_10pcnt:Sex                                         -0.871623763
##                                                                                  97.5 %
## (Intercept)                                                                708.82857274
## Natural_environment_300m_10pcnt                                              0.91901592
## Sex                                                                         -5.74701544
## Age                                                                        -16.18334738
## BMI                                                                          1.28346765
## EducationCollege or University Degree                                       -0.47329486
## EducationCSEs or equivalent                                                  5.38504639
## EducationNational Vocational Qualification or equivalent                     3.40172002
## EducationNone of the above                                                   7.89594616
## EducationO levels/General Certificate of Secondary Education or equivalent   1.75679774
## EducationOther professional qualifications                                   5.19081940
## Income                                                                       0.40550272
## Average_time_outdoors                                                        0.49533077
## Summed_PA_min                                                                0.01153425
## Smoking                                                                      0.50342862
## Disability                                                                   0.57569114
## Deprivation_Index                                                            0.01313801
## Population_density                                                           0.70581398
## Natural_environment_300m_10pcnt:Sex                                          0.28881206

8.2.3) Moderation by sex: Average hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5921, -0.3081, 0.0226, 0.339, 5.6507
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.982e+00
## Natural_environment_300m_10pcnt                                            -3.667e-03
## Sex                                                                         3.017e-01
## Age                                                                        -2.163e-01
## BMI                                                                        -1.352e-02
## EducationCollege or University Degree                                       2.359e-02
## EducationCSEs or equivalent                                                 5.562e-02
## EducationNational Vocational Qualification or equivalent                    5.863e-02
## EducationNone of the above                                                  5.469e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.742e-02
## EducationOther professional qualifications                                  1.703e-02
## Income                                                                     -2.795e-04
## Average_time_outdoors                                                       2.942e-05
## Summed_PA_min                                                               6.303e-05
## Smoking                                                                    -3.815e-02
## Disability                                                                 -2.211e-02
## Deprivation_Index                                                           6.749e-05
## Population_density                                                          9.860e-04
## Natural_environment_300m_10pcnt:Sex                                        -5.897e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.772e-02
## Natural_environment_300m_10pcnt                                             2.694e-03
## Sex                                                                         1.834e-02
## Age                                                                         7.110e-03
## BMI                                                                         5.955e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.119e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.990e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.869e-03
## Average_time_outdoors                                                       3.475e-03
## Summed_PA_min                                                               5.983e-05
## Smoking                                                                     8.209e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.438e-04
## Population_density                                                          1.075e-02
## Natural_environment_300m_10pcnt:Sex                                         4.036e-03
##                                                                            t value
## (Intercept)                                                                179.717
## Natural_environment_300m_10pcnt                                             -1.361
## Sex                                                                         16.453
## Age                                                                        -30.418
## BMI                                                                         -2.270
## EducationCollege or University Degree                                        1.571
## EducationCSEs or equivalent                                                  1.783
## EducationNational Vocational Qualification or equivalent                     2.198
## EducationNone of the above                                                   1.829
## EducationO levels/General Certificate of Secondary Education or equivalent   2.121
## EducationOther professional qualifications                                   0.622
## Income                                                                      -0.057
## Average_time_outdoors                                                        0.008
## Summed_PA_min                                                                1.053
## Smoking                                                                     -4.648
## Disability                                                                  -1.866
## Deprivation_Index                                                            0.196
## Population_density                                                           0.092
## Natural_environment_300m_10pcnt:Sex                                         -1.461
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.1735
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0232
## EducationCollege or University Degree                                        0.1162
## EducationCSEs or equivalent                                                  0.0746
## EducationNational Vocational Qualification or equivalent                     0.0280
## EducationNone of the above                                                   0.0674
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0340
## EducationOther professional qualifications                                   0.5336
## Income                                                                       0.9542
## Average_time_outdoors                                                        0.9932
## Summed_PA_min                                                                0.2922
## Smoking                                                                     3.4e-06
## Disability                                                                   0.0621
## Deprivation_Index                                                            0.8444
## Population_density                                                           0.9269
## Natural_environment_300m_10pcnt:Sex                                          0.1440
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11423 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1659, Adjusted R-squared:  0.1646 
## F-statistic: 126.2 on 18 and 11423 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.927522e+00
## Natural_environment_300m_10pcnt                                            -8.947999e-03
## Sex                                                                         2.657469e-01
## Age                                                                        -2.301970e-01
## BMI                                                                        -2.519311e-02
## EducationCollege or University Degree                                      -5.840527e-03
## EducationCSEs or equivalent                                                -5.525986e-03
## EducationNational Vocational Qualification or equivalent                    6.332961e-03
## EducationNone of the above                                                 -3.923410e-03
## EducationO levels/General Certificate of Secondary Education or equivalent  2.835479e-03
## EducationOther professional qualifications                                 -3.660672e-02
## Income                                                                     -9.823552e-03
## Average_time_outdoors                                                      -6.781391e-03
## Summed_PA_min                                                              -5.425223e-05
## Smoking                                                                    -5.424543e-02
## Disability                                                                 -4.533609e-02
## Deprivation_Index                                                          -6.063929e-04
## Population_density                                                         -2.008600e-02
## Natural_environment_300m_10pcnt:Sex                                        -1.380931e-02
##                                                                                   97.5 %
## (Intercept)                                                                 5.0361962188
## Natural_environment_300m_10pcnt                                             0.0016138868
## Sex                                                                         0.3376344881
## Age                                                                        -0.2023247699
## BMI                                                                        -0.0018456401
## EducationCollege or University Degree                                       0.0530300208
## EducationCSEs or equivalent                                                 0.1167645078
## EducationNational Vocational Qualification or equivalent                    0.1109274598
## EducationNone of the above                                                  0.1133110874
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0719997554
## EducationOther professional qualifications                                  0.0706763056
## Income                                                                      0.0092644806
## Average_time_outdoors                                                       0.0068402291
## Summed_PA_min                                                               0.0001803112
## Smoking                                                                    -0.0220618422
## Disability                                                                  0.0011159564
## Deprivation_Index                                                           0.0007413762
## Population_density                                                          0.0220579289
## Natural_environment_300m_10pcnt:Sex                                         0.0020149743

9) Sensitivity analyses for cognitive function

9.1) Greenspace percentage instead of natural environment percentage

9.1.1) 1000m greenspace buffer

Association of greenspace (buffered to 1000m) with Trail-making Test (B-A) (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Trails_B_A~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Greenspace_1000m_10pcnt + Age + Sex + 
##     BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.821, -10.259, -2.526, 6.973, 176.427
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                27.85302
## Greenspace_1000m_10pcnt                                                    -0.10698
## Age                                                                         4.21062
## Sex                                                                         0.11492
## BMI                                                                         0.14506
## EducationCollege or University Degree                                      -0.62401
## EducationCSEs or equivalent                                                 4.51550
## EducationNational Vocational Qualification or equivalent                    7.06351
## EducationNone of the above                                                 10.32567
## EducationO levels/General Certificate of Secondary Education or equivalent  1.82953
## EducationOther professional qualifications                                  3.60467
## Income                                                                     -0.92593
##                                                                            Std. Error
## (Intercept)                                                                   0.71153
## Greenspace_1000m_10pcnt                                                       0.06396
## Age                                                                           0.23859
## Sex                                                                           0.34263
## BMI                                                                           0.19887
## EducationCollege or University Degree                                         0.50709
## EducationCSEs or equivalent                                                   1.05007
## EducationNational Vocational Qualification or equivalent                      0.90018
## EducationNone of the above                                                    1.00495
## EducationO levels/General Certificate of Secondary Education or equivalent    0.59533
## EducationOther professional qualifications                                    0.92457
## Income                                                                        0.16239
##                                                                            t value
## (Intercept)                                                                 39.145
## Greenspace_1000m_10pcnt                                                     -1.673
## Age                                                                         17.648
## Sex                                                                          0.335
## BMI                                                                          0.729
## EducationCollege or University Degree                                       -1.231
## EducationCSEs or equivalent                                                  4.300
## EducationNational Vocational Qualification or equivalent                     7.847
## EducationNone of the above                                                  10.275
## EducationO levels/General Certificate of Secondary Education or equivalent   3.073
## EducationOther professional qualifications                                   3.899
## Income                                                                      -5.702
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                     0.09443
## Age                                                                         < 2e-16
## Sex                                                                         0.73734
## BMI                                                                         0.46576
## EducationCollege or University Degree                                       0.21851
## EducationCSEs or equivalent                                                1.72e-05
## EducationNational Vocational Qualification or equivalent                   4.65e-15
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00212
## EducationOther professional qualifications                                 9.72e-05
## Income                                                                     1.22e-08
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    .  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.74 on 11436 degrees of freedom
## Multiple R-squared:  0.06943,    Adjusted R-squared:  0.06853 
## F-statistic: 77.56 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                 2.5 %
## (Intercept)                                                                26.4583038
## Greenspace_1000m_10pcnt                                                    -0.2323501
## Age                                                                         3.7429453
## Sex                                                                        -0.5566998
## BMI                                                                        -0.2447626
## EducationCollege or University Degree                                      -1.6179822
## EducationCSEs or equivalent                                                 2.4571783
## EducationNational Vocational Qualification or equivalent                    5.2989936
## EducationNone of the above                                                  8.3558008
## EducationO levels/General Certificate of Secondary Education or equivalent  0.6625884
## EducationOther professional qualifications                                  1.7923456
## Income                                                                     -1.2442497
##                                                                                 97.5 %
## (Intercept)                                                                29.24774575
## Greenspace_1000m_10pcnt                                                     0.01839085
## Age                                                                         4.67830046
## Sex                                                                         0.78653041
## BMI                                                                         0.53488866
## EducationCollege or University Degree                                       0.36996908
## EducationCSEs or equivalent                                                 6.57382388
## EducationNational Vocational Qualification or equivalent                    8.82801702
## EducationNone of the above                                                 12.29554405
## EducationO levels/General Certificate of Secondary Education or equivalent  2.99647281
## EducationOther professional qualifications                                  5.41698832
## Income                                                                     -0.60760606

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Trails_B_A~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Greenspace_1000m_10pcnt + Age + Sex + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -135.156, -10.208, -2.52, 6.957, 175.511
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.097925
## Greenspace_1000m_10pcnt                                                    -0.149953
## Age                                                                         4.112060
## Sex                                                                         0.266898
## BMI                                                                         0.181304
## EducationCollege or University Degree                                      -0.519889
## EducationCSEs or equivalent                                                 4.167721
## EducationNational Vocational Qualification or equivalent                    6.808285
## EducationNone of the above                                                  9.844473
## EducationO levels/General Certificate of Secondary Education or equivalent  1.695407
## EducationOther professional qualifications                                  3.534087
## Income                                                                     -0.837375
## Average_time_outdoors                                                       0.304358
## Summed_PA_min                                                               0.003365
## Smoking                                                                     0.643310
## Disability                                                                 -0.061973
## Deprivation_Index                                                          -0.037722
## Population_density                                                          0.253469
##                                                                            Std. Error
## (Intercept)                                                                  0.940263
## Greenspace_1000m_10pcnt                                                      0.085470
## Age                                                                          0.240277
## Sex                                                                          0.345736
## BMI                                                                          0.201073
## EducationCollege or University Degree                                        0.507457
## EducationCSEs or equivalent                                                  1.052284
## EducationNational Vocational Qualification or equivalent                     0.900825
## EducationNone of the above                                                   1.009815
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595588
## EducationOther professional qualifications                                   0.924020
## Income                                                                       0.164368
## Average_time_outdoors                                                        0.117284
## Summed_PA_min                                                                0.002020
## Smoking                                                                      0.277522
## Disability                                                                   0.399978
## Deprivation_Index                                                            0.011609
## Population_density                                                           0.364176
##                                                                            t value
## (Intercept)                                                                 27.756
## Greenspace_1000m_10pcnt                                                     -1.754
## Age                                                                         17.114
## Sex                                                                          0.772
## BMI                                                                          0.902
## EducationCollege or University Degree                                       -1.024
## EducationCSEs or equivalent                                                  3.961
## EducationNational Vocational Qualification or equivalent                     7.558
## EducationNone of the above                                                   9.749
## EducationO levels/General Certificate of Secondary Education or equivalent   2.847
## EducationOther professional qualifications                                   3.825
## Income                                                                      -5.095
## Average_time_outdoors                                                        2.595
## Summed_PA_min                                                                1.666
## Smoking                                                                      2.318
## Disability                                                                  -0.155
## Deprivation_Index                                                           -3.249
## Population_density                                                           0.696
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    0.079379
## Age                                                                         < 2e-16
## Sex                                                                        0.440148
## BMI                                                                        0.367245
## EducationCollege or University Degree                                      0.305621
## EducationCSEs or equivalent                                                7.52e-05
## EducationNational Vocational Qualification or equivalent                   4.41e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004427
## EducationOther professional qualifications                                 0.000132
## Income                                                                     3.55e-07
## Average_time_outdoors                                                      0.009470
## Summed_PA_min                                                              0.095835
## Smoking                                                                    0.020464
## Disability                                                                 0.876871
## Deprivation_Index                                                          0.001160
## Population_density                                                         0.486439
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    .  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11430 degrees of freedom
## Multiple R-squared:  0.07196,    Adjusted R-squared:  0.07058 
## F-statistic: 52.13 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.2548475558
## Greenspace_1000m_10pcnt                                                    -0.3174880831
## Age                                                                         3.6410755402
## Sex                                                                        -0.4108043028
## BMI                                                                        -0.2128336233
## EducationCollege or University Degree                                      -1.5145905872
## EducationCSEs or equivalent                                                 2.1050645564
## EducationNational Vocational Qualification or equivalent                    5.0425143462
## EducationNone of the above                                                  7.8650626388
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5279520204
## EducationOther professional qualifications                                  1.7228485273
## Income                                                                     -1.1595638022
## Average_time_outdoors                                                       0.0744612126
## Summed_PA_min                                                              -0.0005953027
## Smoking                                                                     0.0993194714
## Disability                                                                 -0.8459980061
## Deprivation_Index                                                          -0.0604775575
## Population_density                                                         -0.4603790712
##                                                                                  97.5 %
## (Intercept)                                                                27.941002304
## Greenspace_1000m_10pcnt                                                     0.017582398
## Age                                                                         4.583044317
## Sex                                                                         0.944601221
## BMI                                                                         0.575441213
## EducationCollege or University Degree                                       0.474813388
## EducationCSEs or equivalent                                                 6.230378277
## EducationNational Vocational Qualification or equivalent                    8.574055999
## EducationNone of the above                                                 11.823882543
## EducationO levels/General Certificate of Secondary Education or equivalent  2.862861790
## EducationOther professional qualifications                                  5.345324654
## Income                                                                     -0.515186419
## Average_time_outdoors                                                       0.534253984
## Summed_PA_min                                                               0.007325439
## Smoking                                                                     1.187300439
## Disability                                                                  0.722052400
## Deprivation_Index                                                          -0.014966041
## Population_density                                                          0.967316780

Association of greenspace (buffered to 1000m) with Symbol Digit Substitution (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Symbol.Digit~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Greenspace_1000m_10pcnt + Age + Sex + 
##     BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.462, -2.464, 0.29, 2.807, 63.086
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                19.392561
## Greenspace_1000m_10pcnt                                                     0.069188
## Age                                                                        -2.420127
## Sex                                                                         0.021269
## BMI                                                                         0.004732
## EducationCollege or University Degree                                       0.313197
## EducationCSEs or equivalent                                                -1.302586
## EducationNational Vocational Qualification or equivalent                   -0.887817
## EducationNone of the above                                                 -1.591257
## EducationO levels/General Certificate of Secondary Education or equivalent -0.458582
## EducationOther professional qualifications                                 -1.141275
## Income                                                                      0.353957
##                                                                            Std. Error
## (Intercept)                                                                  0.173340
## Greenspace_1000m_10pcnt                                                      0.015581
## Age                                                                          0.058124
## Sex                                                                          0.083470
## BMI                                                                          0.048449
## EducationCollege or University Degree                                        0.123534
## EducationCSEs or equivalent                                                  0.255814
## EducationNational Vocational Qualification or equivalent                     0.219298
## EducationNone of the above                                                   0.244821
## EducationO levels/General Certificate of Secondary Education or equivalent   0.145031
## EducationOther professional qualifications                                   0.225240
## Income                                                                       0.039562
##                                                                            t value
## (Intercept)                                                                111.876
## Greenspace_1000m_10pcnt                                                      4.440
## Age                                                                        -41.637
## Sex                                                                          0.255
## BMI                                                                          0.098
## EducationCollege or University Degree                                        2.535
## EducationCSEs or equivalent                                                 -5.092
## EducationNational Vocational Qualification or equivalent                    -4.048
## EducationNone of the above                                                  -6.500
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.162
## EducationOther professional qualifications                                  -5.067
## Income                                                                       8.947
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    9.06e-06
## Age                                                                         < 2e-16
## Sex                                                                         0.79888
## BMI                                                                         0.92220
## EducationCollege or University Degree                                       0.01125
## EducationCSEs or equivalent                                                3.60e-07
## EducationNational Vocational Qualification or equivalent                   5.19e-05
## EducationNone of the above                                                 8.38e-11
## EducationO levels/General Certificate of Secondary Education or equivalent  0.00157
## EducationOther professional qualifications                                 4.11e-07
## Income                                                                      < 2e-16
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.322 on 11436 degrees of freedom
## Multiple R-squared:  0.1925, Adjusted R-squared:  0.1918 
## F-statistic: 247.9 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                19.05278532
## Greenspace_1000m_10pcnt                                                     0.03864603
## Age                                                                        -2.53406054
## Sex                                                                        -0.14234699
## BMI                                                                        -0.09023593
## EducationCollege or University Degree                                       0.07104959
## EducationCSEs or equivalent                                                -1.80402508
## EducationNational Vocational Qualification or equivalent                   -1.31767921
## EducationNone of the above                                                 -2.07114768
## EducationO levels/General Certificate of Secondary Education or equivalent -0.74286654
## EducationOther professional qualifications                                 -1.58278370
## Income                                                                      0.27640893
##                                                                                 97.5 %
## (Intercept)                                                                19.73233589
## Greenspace_1000m_10pcnt                                                     0.09973035
## Age                                                                        -2.30619377
## Sex                                                                         0.18488435
## BMI                                                                         0.09969900
## EducationCollege or University Degree                                       0.55534481
## EducationCSEs or equivalent                                                -0.80114750
## EducationNational Vocational Qualification or equivalent                   -0.45795532
## EducationNone of the above                                                 -1.11136620
## EducationO levels/General Certificate of Secondary Education or equivalent -0.17429673
## EducationOther professional qualifications                                 -0.69976551
## Income                                                                      0.43150502

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Symbol.Digit~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Greenspace_1000m_10pcnt + Age + Sex + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.939, -2.479, 0.281, 2.777, 63.341
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                20.491985
## Greenspace_1000m_10pcnt                                                     0.105551
## Age                                                                        -2.358692
## Sex                                                                        -0.067079
## BMI                                                                        -0.002825
## EducationCollege or University Degree                                       0.274235
## EducationCSEs or equivalent                                                -1.128057
## EducationNational Vocational Qualification or equivalent                   -0.779080
## EducationNone of the above                                                 -1.363879
## EducationO levels/General Certificate of Secondary Education or equivalent -0.392829
## EducationOther professional qualifications                                 -1.079216
## Income                                                                      0.305087
## Average_time_outdoors                                                      -0.185128
## Summed_PA_min                                                              -0.001461
## Smoking                                                                    -0.129322
## Disability                                                                 -0.241808
## Deprivation_Index                                                          -0.001370
## Population_density                                                         -0.192041
##                                                                            Std. Error
## (Intercept)                                                                  0.228490
## Greenspace_1000m_10pcnt                                                      0.020770
## Age                                                                          0.058389
## Sex                                                                          0.084016
## BMI                                                                          0.048862
## EducationCollege or University Degree                                        0.123315
## EducationCSEs or equivalent                                                  0.255711
## EducationNational Vocational Qualification or equivalent                     0.218906
## EducationNone of the above                                                   0.245391
## EducationO levels/General Certificate of Secondary Education or equivalent   0.144732
## EducationOther professional qualifications                                   0.224542
## Income                                                                       0.039942
## Average_time_outdoors                                                        0.028501
## Summed_PA_min                                                                0.000491
## Smoking                                                                      0.067439
## Disability                                                                   0.097197
## Deprivation_Index                                                            0.002821
## Population_density                                                           0.088497
##                                                                            t value
## (Intercept)                                                                 89.685
## Greenspace_1000m_10pcnt                                                      5.082
## Age                                                                        -40.396
## Sex                                                                         -0.798
## BMI                                                                         -0.058
## EducationCollege or University Degree                                        2.224
## EducationCSEs or equivalent                                                 -4.411
## EducationNational Vocational Qualification or equivalent                    -3.559
## EducationNone of the above                                                  -5.558
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.714
## EducationOther professional qualifications                                  -4.806
## Income                                                                       7.638
## Average_time_outdoors                                                       -6.496
## Summed_PA_min                                                               -2.976
## Smoking                                                                     -1.918
## Disability                                                                  -2.488
## Deprivation_Index                                                           -0.486
## Population_density                                                          -2.170
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    3.79e-07
## Age                                                                         < 2e-16
## Sex                                                                        0.424652
## BMI                                                                        0.953889
## EducationCollege or University Degree                                      0.026177
## EducationCSEs or equivalent                                                1.04e-05
## EducationNational Vocational Qualification or equivalent                   0.000374
## EducationNone of the above                                                 2.79e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.006654
## EducationOther professional qualifications                                 1.56e-06
## Income                                                                     2.38e-14
## Average_time_outdoors                                                      8.62e-11
## Summed_PA_min                                                              0.002923
## Smoking                                                                    0.055187
## Disability                                                                 0.012867
## Deprivation_Index                                                          0.627131
## Population_density                                                         0.030025
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    .  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                         *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.307 on 11430 degrees of freedom
## Multiple R-squared:  0.1987, Adjusted R-squared:  0.1976 
## F-statistic: 166.8 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.044105873
## Greenspace_1000m_10pcnt                                                     0.064838872
## Age                                                                        -2.473144014
## Sex                                                                        -0.231764690
## BMI                                                                        -0.098603168
## EducationCollege or University Degree                                       0.032516845
## EducationCSEs or equivalent                                                -1.629295457
## EducationNational Vocational Qualification or equivalent                   -1.208173193
## EducationNone of the above                                                 -1.844887905
## EducationO levels/General Certificate of Secondary Education or equivalent -0.676527447
## EducationOther professional qualifications                                 -1.519357229
## Income                                                                      0.226793362
## Average_time_outdoors                                                      -0.240994030
## Summed_PA_min                                                              -0.002423730
## Smoking                                                                    -0.261514568
## Disability                                                                 -0.432330408
## Deprivation_Index                                                          -0.006900209
## Population_density                                                         -0.365510320
##                                                                                   97.5 %
## (Intercept)                                                                20.9398634854
## Greenspace_1000m_10pcnt                                                     0.1462629994
## Age                                                                        -2.2442399767
## Sex                                                                         0.0976069450
## BMI                                                                         0.0929523238
## EducationCollege or University Degree                                       0.5159538892
## EducationCSEs or equivalent                                                -0.6268195920
## EducationNational Vocational Qualification or equivalent                   -0.3499874859
## EducationNone of the above                                                 -0.8828710321
## EducationO levels/General Certificate of Secondary Education or equivalent -0.1091304325
## EducationOther professional qualifications                                 -0.6390739021
## Income                                                                      0.3833809132
## Average_time_outdoors                                                      -0.1292616413
## Summed_PA_min                                                              -0.0004989428
## Smoking                                                                     0.0028713031
## Disability                                                                 -0.0512847973
## Deprivation_Index                                                           0.0041593609
## Population_density                                                         -0.0185717037

Moderation by sex: association of greenspace (buffered to 1000m) with TMT (B-A) (not significant)

summary_confint(lm(Trails_B_A~Greenspace_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Greenspace_1000m_10pcnt * Sex + Age + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.849, -10.23, -2.519, 6.963, 175.651
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.096344
## Greenspace_1000m_10pcnt                                                    -0.152325
## Sex                                                                        -0.428128
## Age                                                                         4.114311
## BMI                                                                         0.181422
## EducationCollege or University Degree                                      -0.513963
## EducationCSEs or equivalent                                                 4.179435
## EducationNational Vocational Qualification or equivalent                    6.820877
## EducationNone of the above                                                  9.827129
## EducationO levels/General Certificate of Secondary Education or equivalent  1.692842
## EducationOther professional qualifications                                  3.531675
## Income                                                                     -0.836990
## Average_time_outdoors                                                       0.307495
## Summed_PA_min                                                               0.003363
## Smoking                                                                     0.645205
## Disability                                                                 -0.060812
## Deprivation_Index                                                          -0.037693
## Population_density                                                          0.255447
## Greenspace_1000m_10pcnt:Sex                                                 0.157495
##                                                                            Std. Error
## (Intercept)                                                                  0.940242
## Greenspace_1000m_10pcnt                                                      0.085489
## Sex                                                                          0.659709
## Age                                                                          0.240278
## BMI                                                                          0.201068
## EducationCollege or University Degree                                        0.507467
## EducationCSEs or equivalent                                                  1.052302
## EducationNational Vocational Qualification or equivalent                     0.900861
## EducationNone of the above                                                   1.009889
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595578
## EducationOther professional qualifications                                   0.924001
## Income                                                                       0.164364
## Average_time_outdoors                                                        0.117309
## Summed_PA_min                                                                0.002020
## Smoking                                                                      0.277520
## Disability                                                                   0.399970
## Deprivation_Index                                                            0.011609
## Population_density                                                           0.364171
## Greenspace_1000m_10pcnt:Sex                                                  0.127320
##                                                                            t value
## (Intercept)                                                                 27.755
## Greenspace_1000m_10pcnt                                                     -1.782
## Sex                                                                         -0.649
## Age                                                                         17.123
## BMI                                                                          0.902
## EducationCollege or University Degree                                       -1.013
## EducationCSEs or equivalent                                                  3.972
## EducationNational Vocational Qualification or equivalent                     7.572
## EducationNone of the above                                                   9.731
## EducationO levels/General Certificate of Secondary Education or equivalent   2.842
## EducationOther professional qualifications                                   3.822
## Income                                                                      -5.092
## Average_time_outdoors                                                        2.621
## Summed_PA_min                                                                1.664
## Smoking                                                                      2.325
## Disability                                                                  -0.152
## Deprivation_Index                                                           -3.247
## Population_density                                                           0.701
## Greenspace_1000m_10pcnt:Sex                                                  1.237
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    0.074808
## Sex                                                                        0.516374
## Age                                                                         < 2e-16
## BMI                                                                        0.366921
## EducationCollege or University Degree                                      0.311178
## EducationCSEs or equivalent                                                7.18e-05
## EducationNational Vocational Qualification or equivalent                   3.97e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004486
## EducationOther professional qualifications                                 0.000133
## Income                                                                     3.59e-07
## Average_time_outdoors                                                      0.008772
## Summed_PA_min                                                              0.096072
## Smoking                                                                    0.020095
## Disability                                                                 0.879158
## Deprivation_Index                                                          0.001170
## Population_density                                                         0.483038
## Greenspace_1000m_10pcnt:Sex                                                0.216110
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    .  
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ** 
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Greenspace_1000m_10pcnt:Sex                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11429 degrees of freedom
## Multiple R-squared:  0.07208,    Adjusted R-squared:  0.07062 
## F-statistic: 49.32 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.2533078295
## Greenspace_1000m_10pcnt                                                    -0.3198984080
## Sex                                                                        -1.7212706650
## Age                                                                         3.6433236401
## BMI                                                                        -0.2127060155
## EducationCollege or University Degree                                      -1.5086858032
## EducationCSEs or equivalent                                                 2.1167420372
## EducationNational Vocational Qualification or equivalent                    5.0550346402
## EducationNone of the above                                                  7.8475738162
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5254074736
## EducationOther professional qualifications                                  1.7204750243
## Income                                                                     -1.1591714134
## Average_time_outdoors                                                       0.0775499472
## Summed_PA_min                                                              -0.0005976882
## Smoking                                                                     0.1012184694
## Disability                                                                 -0.8448207490
## Deprivation_Index                                                          -0.0604479809
## Population_density                                                         -0.4583913948
## Greenspace_1000m_10pcnt:Sex                                                -0.0920729917
##                                                                                  97.5 %
## (Intercept)                                                                27.939380527
## Greenspace_1000m_10pcnt                                                     0.015248627
## Sex                                                                         0.865015224
## Age                                                                         4.585297586
## BMI                                                                         0.575550636
## EducationCollege or University Degree                                       0.480760703
## EducationCSEs or equivalent                                                 6.242127141
## EducationNational Vocational Qualification or equivalent                    8.586719899
## EducationNone of the above                                                 11.806683530
## EducationO levels/General Certificate of Secondary Education or equivalent  2.860277260
## EducationOther professional qualifications                                  5.342875235
## Income                                                                     -0.514807811
## Average_time_outdoors                                                       0.537439542
## Summed_PA_min                                                               0.007322874
## Smoking                                                                     1.189190785
## Disability                                                                  0.723197624
## Deprivation_Index                                                          -0.014937426
## Population_density                                                          0.969285121
## Greenspace_1000m_10pcnt:Sex                                                 0.407063440

Moderation by sex: association of greenspace (buffered to 1000m) with Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Greenspace_1000m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Greenspace_1000m_10pcnt * Sex + Age + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.946, -2.476, 0.276, 2.766, 63.325
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                20.491790
## Greenspace_1000m_10pcnt                                                     0.105258
## Sex                                                                        -0.152814
## Age                                                                        -2.358414
## BMI                                                                        -0.002811
## EducationCollege or University Degree                                       0.274966
## EducationCSEs or equivalent                                                -1.126613
## EducationNational Vocational Qualification or equivalent                   -0.777527
## EducationNone of the above                                                 -1.366019
## EducationO levels/General Certificate of Secondary Education or equivalent -0.393145
## EducationOther professional qualifications                                 -1.079513
## Income                                                                      0.305135
## Average_time_outdoors                                                      -0.184741
## Summed_PA_min                                                              -0.001462
## Smoking                                                                    -0.129088
## Disability                                                                 -0.241664
## Deprivation_Index                                                          -0.001367
## Population_density                                                         -0.191797
## Greenspace_1000m_10pcnt:Sex                                                 0.019428
##                                                                            Std. Error
## (Intercept)                                                                  0.228496
## Greenspace_1000m_10pcnt                                                      0.020775
## Sex                                                                          0.160321
## Age                                                                          0.058392
## BMI                                                                          0.048863
## EducationCollege or University Degree                                        0.123324
## EducationCSEs or equivalent                                                  0.255728
## EducationNational Vocational Qualification or equivalent                     0.218925
## EducationNone of the above                                                   0.245421
## EducationO levels/General Certificate of Secondary Education or equivalent   0.144736
## EducationOther professional qualifications                                   0.224549
## Income                                                                       0.039943
## Average_time_outdoors                                                        0.028508
## Summed_PA_min                                                                0.000491
## Smoking                                                                      0.067442
## Disability                                                                   0.097200
## Deprivation_Index                                                            0.002821
## Population_density                                                           0.088500
## Greenspace_1000m_10pcnt:Sex                                                  0.030941
##                                                                            t value
## (Intercept)                                                                 89.681
## Greenspace_1000m_10pcnt                                                      5.066
## Sex                                                                         -0.953
## Age                                                                        -40.389
## BMI                                                                         -0.058
## EducationCollege or University Degree                                        2.230
## EducationCSEs or equivalent                                                 -4.406
## EducationNational Vocational Qualification or equivalent                    -3.552
## EducationNone of the above                                                  -5.566
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.716
## EducationOther professional qualifications                                  -4.807
## Income                                                                       7.639
## Average_time_outdoors                                                       -6.480
## Summed_PA_min                                                               -2.977
## Smoking                                                                     -1.914
## Disability                                                                  -2.486
## Deprivation_Index                                                           -0.484
## Population_density                                                          -2.167
## Greenspace_1000m_10pcnt:Sex                                                  0.628
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    4.12e-07
## Sex                                                                        0.340521
## Age                                                                         < 2e-16
## BMI                                                                        0.954129
## EducationCollege or University Degree                                      0.025791
## EducationCSEs or equivalent                                                1.06e-05
## EducationNational Vocational Qualification or equivalent                   0.000384
## EducationNone of the above                                                 2.66e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.006612
## EducationOther professional qualifications                                 1.55e-06
## Income                                                                     2.36e-14
## Average_time_outdoors                                                      9.53e-11
## Summed_PA_min                                                              0.002917
## Smoking                                                                    0.055639
## Disability                                                                 0.012923
## Deprivation_Index                                                          0.628044
## Population_density                                                         0.030241
## Greenspace_1000m_10pcnt:Sex                                                0.530079
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    .  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                         *  
## Greenspace_1000m_10pcnt:Sex                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.307 on 11429 degrees of freedom
## Multiple R-squared:  0.1988, Adjusted R-squared:  0.1975 
## F-statistic: 157.5 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.043898592
## Greenspace_1000m_10pcnt                                                     0.064534941
## Sex                                                                        -0.467071541
## Age                                                                        -2.472872694
## BMI                                                                        -0.098591098
## EducationCollege or University Degree                                       0.033230679
## EducationCSEs or equivalent                                                -1.627884149
## EducationNational Vocational Qualification or equivalent                   -1.206658655
## EducationNone of the above                                                 -1.847086497
## EducationO levels/General Certificate of Secondary Education or equivalent -0.676853037
## EducationOther professional qualifications                                 -1.519667344
## Income                                                                      0.226838699
## Average_time_outdoors                                                      -0.240621585
## Summed_PA_min                                                              -0.002424062
## Smoking                                                                    -0.261286367
## Disability                                                                 -0.432192737
## Deprivation_Index                                                          -0.006896778
## Population_density                                                         -0.365272591
## Greenspace_1000m_10pcnt:Sex                                                -0.041221611
##                                                                                   97.5 %
## (Intercept)                                                                20.9396807763
## Greenspace_1000m_10pcnt                                                     0.1459817183
## Sex                                                                         0.1614426024
## Age                                                                        -2.2439560260
## BMI                                                                         0.0929694931
## EducationCollege or University Degree                                       0.5167020818
## EducationCSEs or equivalent                                                -0.6253411216
## EducationNational Vocational Qualification or equivalent                   -0.3483954043
## EducationNone of the above                                                 -0.8849513906
## EducationO levels/General Certificate of Secondary Education or equivalent -0.1094375444
## EducationOther professional qualifications                                 -0.6393587233
## Income                                                                      0.3834306829
## Average_time_outdoors                                                      -0.1288601146
## Summed_PA_min                                                              -0.0004992222
## Smoking                                                                     0.0031105397
## Disability                                                                 -0.0511359763
## Deprivation_Index                                                           0.0041631079
## Population_density                                                         -0.0183214340
## Greenspace_1000m_10pcnt:Sex                                                 0.0800775490

9.1.2) 300m greenspace buffer

Association of greenspace (buffered to 300m) with Trail-making Test (B-A) (not significant)

summary_confint(lm(Trails_B_A~Greenspace_300m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Greenspace_300m_10pcnt + Age + Sex + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.707, -10.186, -2.522, 6.904, 175.729
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                25.920192
## Greenspace_300m_10pcnt                                                     -0.007137
## Age                                                                         4.095255
## Sex                                                                         0.281339
## BMI                                                                         0.176747
## EducationCollege or University Degree                                      -0.478158
## EducationCSEs or equivalent                                                 4.173084
## EducationNational Vocational Qualification or equivalent                    6.809806
## EducationNone of the above                                                  9.853349
## EducationO levels/General Certificate of Secondary Education or equivalent  1.683265
## EducationOther professional qualifications                                  3.527324
## Income                                                                     -0.837291
## Average_time_outdoors                                                       0.298970
## Summed_PA_min                                                               0.003334
## Smoking                                                                     0.672333
## Disability                                                                 -0.062050
## Deprivation_Index                                                          -0.037968
## Population_density                                                         -0.149010
##                                                                            Std. Error
## (Intercept)                                                                  0.936241
## Greenspace_300m_10pcnt                                                       0.079988
## Age                                                                          0.240175
## Sex                                                                          0.345688
## BMI                                                                          0.201085
## EducationCollege or University Degree                                        0.507023
## EducationCSEs or equivalent                                                  1.052421
## EducationNational Vocational Qualification or equivalent                     0.901022
## EducationNone of the above                                                   1.009946
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595648
## EducationOther professional qualifications                                   0.924136
## Income                                                                       0.164446
## Average_time_outdoors                                                        0.117345
## Summed_PA_min                                                                0.002021
## Smoking                                                                      0.277217
## Disability                                                                   0.400066
## Deprivation_Index                                                            0.011610
## Population_density                                                           0.348777
##                                                                            t value
## (Intercept)                                                                 27.685
## Greenspace_300m_10pcnt                                                      -0.089
## Age                                                                         17.051
## Sex                                                                          0.814
## BMI                                                                          0.879
## EducationCollege or University Degree                                       -0.943
## EducationCSEs or equivalent                                                  3.965
## EducationNational Vocational Qualification or equivalent                     7.558
## EducationNone of the above                                                   9.756
## EducationO levels/General Certificate of Secondary Education or equivalent   2.826
## EducationOther professional qualifications                                   3.817
## Income                                                                      -5.092
## Average_time_outdoors                                                        2.548
## Summed_PA_min                                                                1.650
## Smoking                                                                      2.425
## Disability                                                                  -0.155
## Deprivation_Index                                                           -3.270
## Population_density                                                          -0.427
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                     0.928900
## Age                                                                         < 2e-16
## Sex                                                                        0.415747
## BMI                                                                        0.379437
## EducationCollege or University Degree                                      0.345665
## EducationCSEs or equivalent                                                7.38e-05
## EducationNational Vocational Qualification or equivalent                   4.41e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004722
## EducationOther professional qualifications                                 0.000136
## Income                                                                     3.61e-07
## Average_time_outdoors                                                      0.010854
## Summed_PA_min                                                              0.098958
## Smoking                                                                    0.015311
## Disability                                                                 0.876746
## Deprivation_Index                                                          0.001078
## Population_density                                                         0.669216
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      *  
## Summed_PA_min                                                              .  
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.73 on 11430 degrees of freedom
## Multiple R-squared:  0.07171,    Adjusted R-squared:  0.07033 
## F-statistic: 51.94 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.0849989812
## Greenspace_300m_10pcnt                                                     -0.1639279815
## Age                                                                         3.6244702455
## Sex                                                                        -0.3962690709
## BMI                                                                        -0.2174133964
## EducationCollege or University Degree                                      -1.4720104297
## EducationCSEs or equivalent                                                 2.1101582158
## EducationNational Vocational Qualification or equivalent                    5.0436487705
## EducationNone of the above                                                  7.8736813625
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5156918778
## EducationOther professional qualifications                                  1.7158578897
## Income                                                                     -1.1596324687
## Average_time_outdoors                                                       0.0689530985
## Summed_PA_min                                                              -0.0006266216
## Smoking                                                                     0.1289401205
## Disability                                                                 -0.8462472918
## Deprivation_Index                                                          -0.0607248447
## Population_density                                                         -0.8326718755
##                                                                                  97.5 %
## (Intercept)                                                                27.755385773
## Greenspace_300m_10pcnt                                                      0.149653234
## Age                                                                         4.566040397
## Sex                                                                         0.958946817
## BMI                                                                         0.570908062
## EducationCollege or University Degree                                       0.515694079
## EducationCSEs or equivalent                                                 6.236009656
## EducationNational Vocational Qualification or equivalent                    8.575962841
## EducationNone of the above                                                 11.833016978
## EducationO levels/General Certificate of Secondary Education or equivalent  2.850837134
## EducationOther professional qualifications                                  5.338789385
## Income                                                                     -0.514949189
## Average_time_outdoors                                                       0.528986731
## Summed_PA_min                                                               0.007294949
## Smoking                                                                     1.215726133
## Disability                                                                  0.722147923
## Deprivation_Index                                                          -0.015210364
## Population_density                                                          0.534652356

Association of greenspace (buffered to 300m) with Symbol Digit Substitution (not significant)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Symbol.Digit~Greenspace_300m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Greenspace_300m_10pcnt + Age + Sex + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.737, -2.479, 0.278, 2.783, 63.541
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 2.063e+01
## Greenspace_300m_10pcnt                                                      3.110e-02
## Age                                                                        -2.349e+00
## Sex                                                                        -7.660e-02
## BMI                                                                         6.812e-05
## EducationCollege or University Degree                                       2.478e-01
## EducationCSEs or equivalent                                                -1.132e+00
## EducationNational Vocational Qualification or equivalent                   -7.840e-01
## EducationNone of the above                                                 -1.371e+00
## EducationO levels/General Certificate of Secondary Education or equivalent -3.860e-01
## EducationOther professional qualifications                                 -1.075e+00
## Income                                                                      3.036e-01
## Average_time_outdoors                                                      -1.829e-01
## Summed_PA_min                                                              -1.443e-03
## Smoking                                                                    -1.465e-01
## Disability                                                                 -2.435e-01
## Deprivation_Index                                                          -1.189e-03
## Population_density                                                          2.074e-02
##                                                                            Std. Error
## (Intercept)                                                                 2.277e-01
## Greenspace_300m_10pcnt                                                      1.945e-02
## Age                                                                         5.842e-02
## Sex                                                                         8.408e-02
## BMI                                                                         4.891e-02
## EducationCollege or University Degree                                       1.233e-01
## EducationCSEs or equivalent                                                 2.560e-01
## EducationNational Vocational Qualification or equivalent                    2.191e-01
## EducationNone of the above                                                  2.456e-01
## EducationO levels/General Certificate of Secondary Education or equivalent  1.449e-01
## EducationOther professional qualifications                                  2.248e-01
## Income                                                                      4.000e-02
## Average_time_outdoors                                                       2.854e-02
## Summed_PA_min                                                               4.915e-04
## Smoking                                                                     6.742e-02
## Disability                                                                  9.730e-02
## Deprivation_Index                                                           2.824e-03
## Population_density                                                          8.483e-02
##                                                                            t value
## (Intercept)                                                                 90.604
## Greenspace_300m_10pcnt                                                       1.599
## Age                                                                        -40.207
## Sex                                                                         -0.911
## BMI                                                                          0.001
## EducationCollege or University Degree                                        2.009
## EducationCSEs or equivalent                                                 -4.423
## EducationNational Vocational Qualification or equivalent                    -3.577
## EducationNone of the above                                                  -5.583
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.664
## EducationOther professional qualifications                                  -4.781
## Income                                                                       7.591
## Average_time_outdoors                                                       -6.407
## Summed_PA_min                                                               -2.935
## Smoking                                                                     -2.172
## Disability                                                                  -2.502
## Deprivation_Index                                                           -0.421
## Population_density                                                           0.245
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                     0.109949
## Age                                                                         < 2e-16
## Sex                                                                        0.362271
## BMI                                                                        0.998889
## EducationCollege or University Degree                                      0.044556
## EducationCSEs or equivalent                                                9.84e-06
## EducationNational Vocational Qualification or equivalent                   0.000349
## EducationNone of the above                                                 2.42e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.007723
## EducationOther professional qualifications                                 1.76e-06
## Income                                                                     3.41e-14
## Average_time_outdoors                                                      1.55e-10
## Summed_PA_min                                                              0.003339
## Smoking                                                                    0.029848
## Disability                                                                 0.012361
## Deprivation_Index                                                          0.673656
## Population_density                                                         0.806835
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.311 on 11430 degrees of freedom
## Multiple R-squared:  0.1971, Adjusted R-squared:  0.1959 
## F-statistic: 165.1 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.185391515
## Greenspace_300m_10pcnt                                                     -0.007035365
## Age                                                                        -2.463243399
## Sex                                                                        -0.241410563
## BMI                                                                        -0.095799856
## EducationCollege or University Degree                                       0.006026652
## EducationCSEs or equivalent                                                -1.633785618
## EducationNational Vocational Qualification or equivalent                   -1.213533580
## EducationNone of the above                                                 -1.852903343
## EducationO levels/General Certificate of Secondary Education or equivalent -0.669984041
## EducationOther professional qualifications                                 -1.515263542
## Income                                                                      0.225228278
## Average_time_outdoors                                                      -0.238797576
## Summed_PA_min                                                              -0.002405932
## Smoking                                                                    -0.278636746
## Disability                                                                 -0.434195661
## Deprivation_Index                                                          -0.006724237
## Population_density                                                         -0.145538421
##                                                                                  97.5 %
## (Intercept)                                                                21.078104839
## Greenspace_300m_10pcnt                                                      0.069234016
## Age                                                                        -2.234234233
## Sex                                                                         0.088205728
## BMI                                                                         0.095936086
## EducationCollege or University Degree                                       0.489477143
## EducationCSEs or equivalent                                                -0.630293952
## EducationNational Vocational Qualification or equivalent                   -0.354402373
## EducationNone of the above                                                 -0.889911741
## EducationO levels/General Certificate of Secondary Education or equivalent -0.102028835
## EducationOther professional qualifications                                 -0.634092319
## Income                                                                      0.382028470
## Average_time_outdoors                                                      -0.126907964
## Summed_PA_min                                                              -0.000479244
## Smoking                                                                    -0.014308104
## Disability                                                                 -0.052729787
## Deprivation_Index                                                           0.004345817
## Population_density                                                          0.187022867

Moderation by sex: association of greenspace (buffered to 300m) with TMT (B-A) (not significant)

summary_confint(lm(Trails_B_A~Greenspace_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Greenspace_300m_10pcnt * Sex + Age + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.476, -10.198, -2.544, 6.924, 175.96
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                25.921586
## Greenspace_300m_10pcnt                                                     -0.008410
## Sex                                                                        -0.184557
## Age                                                                         4.093829
## BMI                                                                         0.178130
## EducationCollege or University Degree                                      -0.475382
## EducationCSEs or equivalent                                                 4.173112
## EducationNational Vocational Qualification or equivalent                    6.822540
## EducationNone of the above                                                  9.846781
## EducationO levels/General Certificate of Secondary Education or equivalent  1.680614
## EducationOther professional qualifications                                  3.522131
## Income                                                                     -0.836631
## Average_time_outdoors                                                       0.302382
## Summed_PA_min                                                               0.003310
## Smoking                                                                     0.670745
## Disability                                                                 -0.060249
## Deprivation_Index                                                          -0.037974
## Population_density                                                         -0.149518
## Greenspace_300m_10pcnt:Sex                                                  0.158713
##                                                                            Std. Error
## (Intercept)                                                                  0.936216
## Greenspace_300m_10pcnt                                                       0.079992
## Sex                                                                          0.503418
## Age                                                                          0.240172
## BMI                                                                          0.201082
## EducationCollege or University Degree                                        0.507014
## EducationCSEs or equivalent                                                  1.052392
## EducationNational Vocational Qualification or equivalent                     0.901053
## EducationNone of the above                                                   1.009932
## EducationO levels/General Certificate of Secondary Education or equivalent   0.595636
## EducationOther professional qualifications                                   0.924120
## Income                                                                       0.164442
## Average_time_outdoors                                                        0.117373
## Summed_PA_min                                                                0.002021
## Smoking                                                                      0.277212
## Disability                                                                   0.400057
## Deprivation_Index                                                            0.011610
## Population_density                                                           0.348767
## Greenspace_300m_10pcnt:Sex                                                   0.124673
##                                                                            t value
## (Intercept)                                                                 27.688
## Greenspace_300m_10pcnt                                                      -0.105
## Sex                                                                         -0.367
## Age                                                                         17.045
## BMI                                                                          0.886
## EducationCollege or University Degree                                       -0.938
## EducationCSEs or equivalent                                                  3.965
## EducationNational Vocational Qualification or equivalent                     7.572
## EducationNone of the above                                                   9.750
## EducationO levels/General Certificate of Secondary Education or equivalent   2.822
## EducationOther professional qualifications                                   3.811
## Income                                                                      -5.088
## Average_time_outdoors                                                        2.576
## Summed_PA_min                                                                1.638
## Smoking                                                                      2.420
## Disability                                                                  -0.151
## Deprivation_Index                                                           -3.271
## Population_density                                                          -0.429
## Greenspace_300m_10pcnt:Sex                                                   1.273
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                     0.916267
## Sex                                                                        0.713918
## Age                                                                         < 2e-16
## BMI                                                                        0.375713
## EducationCollege or University Degree                                      0.348464
## EducationCSEs or equivalent                                                7.37e-05
## EducationNational Vocational Qualification or equivalent                   3.97e-14
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.004788
## EducationOther professional qualifications                                 0.000139
## Income                                                                     3.68e-07
## Average_time_outdoors                                                      0.010000
## Summed_PA_min                                                              0.101461
## Smoking                                                                    0.015553
## Disability                                                                 0.880293
## Deprivation_Index                                                          0.001075
## Population_density                                                         0.668147
## Greenspace_300m_10pcnt:Sex                                                 0.203032
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      *  
## Summed_PA_min                                                                 
## Smoking                                                                    *  
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Greenspace_300m_10pcnt:Sex                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.72 on 11429 degrees of freedom
## Multiple R-squared:  0.07184,    Adjusted R-squared:  0.07038 
## F-statistic: 49.15 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                24.0864413356
## Greenspace_300m_10pcnt                                                     -0.1652089451
## Sex                                                                        -1.1713425614
## Age                                                                         3.6230512780
## BMI                                                                        -0.2160254212
## EducationCollege or University Degree                                      -1.4692164294
## EducationCSEs or equivalent                                                 2.1102424385
## EducationNational Vocational Qualification or equivalent                    5.0563219654
## EducationNone of the above                                                  7.8671411953
## EducationO levels/General Certificate of Secondary Education or equivalent  0.5130655543
## EducationOther professional qualifications                                  1.7106970308
## Income                                                                     -1.1589654305
## Average_time_outdoors                                                       0.0723117048
## Summed_PA_min                                                              -0.0006511156
## Smoking                                                                     0.1273613967
## Disability                                                                 -0.8444301751
## Deprivation_Index                                                          -0.0607308920
## Population_density                                                         -0.8331620333
## Greenspace_300m_10pcnt:Sex                                                 -0.0856672364
##                                                                                  97.5 %
## (Intercept)                                                                27.756731029
## Greenspace_300m_10pcnt                                                      0.148388263
## Sex                                                                         0.802228733
## Age                                                                         4.564606126
## BMI                                                                         0.572286149
## EducationCollege or University Degree                                       0.518452524
## EducationCSEs or equivalent                                                 6.235981911
## EducationNational Vocational Qualification or equivalent                    8.588757852
## EducationNone of the above                                                 11.826421027
## EducationO levels/General Certificate of Secondary Education or equivalent  2.848161709
## EducationOther professional qualifications                                  5.333565494
## Income                                                                     -0.514296444
## Average_time_outdoors                                                       0.532452862
## Summed_PA_min                                                               0.007270597
## Smoking                                                                     1.214128918
## Disability                                                                  0.723932280
## Deprivation_Index                                                          -0.015217642
## Population_density                                                          0.534125987
## Greenspace_300m_10pcnt:Sex                                                  0.403092708

Moderation by sex: association of greenspace (buffered to 300m) with Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Greenspace_300m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Greenspace_300m_10pcnt * Sex + Age + 
##     BMI + Education + Income + Average_time_outdoors + Summed_PA_min + 
##     Smoking + Disability + Deprivation_Index + Population_density, 
##     data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.732, -2.482, 0.285, 2.782, 63.534
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.6318444
## Greenspace_300m_10pcnt                                                      0.0310114
## Sex                                                                        -0.1087657
## Age                                                                        -2.3488373
## BMI                                                                         0.0001636
## EducationCollege or University Degree                                       0.2479436
## EducationCSEs or equivalent                                                -1.1320378
## EducationNational Vocational Qualification or equivalent                   -0.7830889
## EducationNone of the above                                                 -1.3718610
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3861894
## EducationOther professional qualifications                                 -1.0750364
## Income                                                                      0.3036739
## Average_time_outdoors                                                      -0.1826172
## Summed_PA_min                                                              -0.0014443
## Smoking                                                                    -0.1465821
## Disability                                                                 -0.2433384
## Deprivation_Index                                                          -0.0011897
## Population_density                                                          0.0207071
## Greenspace_300m_10pcnt:Sex                                                  0.0109568
##                                                                            Std. Error
## (Intercept)                                                                 0.2277219
## Greenspace_300m_10pcnt                                                      0.0194570
## Sex                                                                         0.1224496
## Age                                                                         0.0584185
## BMI                                                                         0.0489105
## EducationCollege or University Degree                                       0.1233242
## EducationCSEs or equivalent                                                 0.2559801
## EducationNational Vocational Qualification or equivalent                    0.2191688
## EducationNone of the above                                                  0.2456522
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1448802
## EducationOther professional qualifications                                  0.2247796
## Income                                                                      0.0399983
## Average_time_outdoors                                                       0.0285493
## Summed_PA_min                                                               0.0004915
## Smoking                                                                     0.0674281
## Disability                                                                  0.0973085
## Deprivation_Index                                                           0.0028239
## Population_density                                                          0.0848329
## Greenspace_300m_10pcnt:Sex                                                  0.0303249
##                                                                            t value
## (Intercept)                                                                 90.601
## Greenspace_300m_10pcnt                                                       1.594
## Sex                                                                         -0.888
## Age                                                                        -40.207
## BMI                                                                          0.003
## EducationCollege or University Degree                                        2.011
## EducationCSEs or equivalent                                                 -4.422
## EducationNational Vocational Qualification or equivalent                    -3.573
## EducationNone of the above                                                  -5.585
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.666
## EducationOther professional qualifications                                  -4.783
## Income                                                                       7.592
## Average_time_outdoors                                                       -6.397
## Summed_PA_min                                                               -2.939
## Smoking                                                                     -2.174
## Disability                                                                  -2.501
## Deprivation_Index                                                           -0.421
## Population_density                                                           0.244
## Greenspace_300m_10pcnt:Sex                                                   0.361
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                     0.110999
## Sex                                                                        0.374425
## Age                                                                         < 2e-16
## BMI                                                                        0.997331
## EducationCollege or University Degree                                      0.044402
## EducationCSEs or equivalent                                                9.85e-06
## EducationNational Vocational Qualification or equivalent                   0.000354
## EducationNone of the above                                                 2.40e-08
## EducationO levels/General Certificate of Secondary Education or equivalent 0.007696
## EducationOther professional qualifications                                 1.75e-06
## Income                                                                     3.39e-14
## Average_time_outdoors                                                      1.65e-10
## Summed_PA_min                                                              0.003305
## Smoking                                                                    0.029733
## Disability                                                                 0.012409
## Deprivation_Index                                                          0.673549
## Population_density                                                         0.807163
## Greenspace_300m_10pcnt:Sex                                                 0.717872
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent ** 
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    *  
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_300m_10pcnt:Sex                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.311 on 11429 degrees of freedom
## Multiple R-squared:  0.1971, Adjusted R-squared:  0.1959 
## F-statistic: 155.9 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.185470450
## Greenspace_300m_10pcnt                                                     -0.007127676
## Sex                                                                        -0.348787895
## Age                                                                        -2.463347489
## BMI                                                                        -0.095709424
## EducationCollege or University Degree                                       0.006206877
## EducationCSEs or equivalent                                                -1.633802757
## EducationNational Vocational Qualification or equivalent                   -1.212697292
## EducationNone of the above                                                 -1.853381374
## EducationO levels/General Certificate of Secondary Education or equivalent -0.670179585
## EducationOther professional qualifications                                 -1.515643054
## Income                                                                      0.225270462
## Average_time_outdoors                                                      -0.238578725
## Summed_PA_min                                                              -0.002407699
## Smoking                                                                    -0.278752738
## Disability                                                                 -0.434079795
## Deprivation_Index                                                          -0.006724909
## Population_density                                                         -0.145579945
## Greenspace_300m_10pcnt:Sex                                                 -0.048485288
##                                                                                  97.5 %
## (Intercept)                                                                21.078218348
## Greenspace_300m_10pcnt                                                      0.069150567
## Sex                                                                         0.131256399
## Age                                                                        -2.234327117
## BMI                                                                         0.096036611
## EducationCollege or University Degree                                       0.489680234
## EducationCSEs or equivalent                                                -0.630272914
## EducationNational Vocational Qualification or equivalent                   -0.353480452
## EducationNone of the above                                                 -0.890340568
## EducationO levels/General Certificate of Secondary Education or equivalent -0.102199300
## EducationOther professional qualifications                                 -0.634429723
## Income                                                                      0.382077398
## Average_time_outdoors                                                      -0.126655666
## Summed_PA_min                                                              -0.000480850
## Smoking                                                                    -0.014411364
## Disability                                                                 -0.052597023
## Deprivation_Index                                                           0.004345569
## Population_density                                                          0.186994214
## Greenspace_300m_10pcnt:Sex                                                  0.070398901

9.2) Restrict sample to participants with no change in home location between baseline (2006–2010) and online cognitive assessment (2014-2015, individual-specific dates)

Required UKB variables: * 699 - Length of time at current address - Instances 0 and 2 (unit: years) * 53 - Date of attending assessment centre - Instances 0 and 2 (format: YYYY-MM-DD) Approach: Include if var 699 (Instance) >= Difference in 53 (Instance 2 minus Instance 0) Note: This is a conservative estimate of the subset of participants with no change in home address between baseline and 2014-2015. We were unable to use the actual dates of the online cognitive assessment (var 20136 and 20137; below) because variable 699 was not collected at the same time as the online cognitive assessment; the nearest time at which variable 699 was collected is Instance 2. * 20136 - When trail making test completed * 20137 - When symbol digit substitution test completed

#convert dates to date data type
CogsBrainCov.df2$Date_attending_centre_0 <- as.Date(CogsBrainCov.df2$Date.attending.centre.0)
CogsBrainCov.df2$Date_attending_centre_2 <- as.Date(CogsBrainCov.df2$Date.attending.centre.2)
CogsBrainCov.df2$Date_attending_centre_3 <- as.Date(CogsBrainCov.df2$Date.attending.centre.3)

#include only observations with no missing data for Var 699 and Var 53
HomeChangeTest_T2 <- subset(CogsBrainCov.df2, !is.na(Date_attending_centre_0) & !is.na(Date_attending_centre_2) & !is.na(Time_at_current_address_T2))
length(HomeChangeTest_T2$ID)
## [1] 11389
#include only observations with no change in address between T2 and T0
NoHomeChange_T2 <- subset(HomeChangeTest_T2,Time_at_current_address_T2 >= (round(as.numeric(Date_attending_centre_2 - Date_attending_centre_0) / 365, digits = 0)))
  #more stringent version, where time difference between T2 and T0 is not rounded:
  # NoHomeChange_T2 <- subset(HomeChangeTest_T2,Time_at_current_address_T2 >= (as.numeric(Date_attending_centre_2 - Date_attending_centre_0) / 365, digits = 0))
length(NoHomeChange_T2$ID)
## [1] 9168

Compare the analytical cognitive+brain+covariate data set to the restricted data set with no change in home location

#use CogsBrainCov.df because variables (such as age, BMI, natural environment) are not yet re-scaled

#convert dates to date data type
CogsBrainCov.df$Date_attending_centre_0 <- as.Date(CogsBrainCov.df$Date.attending.centre.0)
CogsBrainCov.df$Date_attending_centre_2 <- as.Date(CogsBrainCov.df$Date.attending.centre.2)
CogsBrainCov.df$Date_attending_centre_3 <- as.Date(CogsBrainCov.df$Date.attending.centre.3)

#include only observations with no missing data for Var 699 and Var 53
HomeChangeTest_T2_unscaled <- subset(CogsBrainCov.df, !is.na(Date_attending_centre_0) & !is.na(Date_attending_centre_2) & !is.na(Time_at_current_address_T2))

#include only observations with no change in address between T2 and T0
NoHomeChange_T2_unscaled <- subset(HomeChangeTest_T2_unscaled,Time_at_current_address_T2 >= (round(as.numeric(Date_attending_centre_2 - Date_attending_centre_0) / 365, digits = 0)))

NoHomeChange_T2_unscaled$included<-"Participants with no change in home location"

AnalyticalVsNoHomeChange<-rbind(CogsBrainCov.df, NoHomeChange_T2_unscaled)

vars2<- subset(AnalyticalVsNoHomeChange, select = c(2:44, 49))

vars2 %>% tbl_summary(
  statistic = list(all_continuous() ~ "{mean} ({sd})",
                   all_categorical() ~ "{n} ({p}%)"),
  digits = all_continuous() ~ 2,
  by = "included"
)

Table for restricted sample with no change in home location, stratified by sex

library(dplyr)

tbl_summary(
  select(NoHomeChange_T2_unscaled, c(2:43)),
  by = "Sex", 
  statistic = list(all_continuous() ~ "{mean} ({sd})",
                   all_categorical() ~ "{n} ({p}%)"),
  digits = all_continuous() ~ 2
) %>%
  add_p(test = list(all_continuous() ~ "t.test",
                   all_categorical() ~ "chisq.test"))

9.2.1) 1000m natural environment buffer

Association of natural environment with Trail-making Test (B-A) (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Trails_B_A~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.542, -10.378, -2.445, 7.069, 176.524
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                28.33421
## Natural_environment_1000m_10pcnt                                           -0.12617
## Age                                                                         4.16635
## Sex                                                                        -0.06555
## BMI                                                                         0.19172
## EducationCollege or University Degree                                      -0.66821
## EducationCSEs or equivalent                                                 4.25952
## EducationNational Vocational Qualification or equivalent                    7.47783
## EducationNone of the above                                                 10.14641
## EducationO levels/General Certificate of Secondary Education or equivalent  1.60136
## EducationOther professional qualifications                                  3.49815
## Income                                                                     -1.03069
##                                                                            Std. Error
## (Intercept)                                                                   0.84084
## Natural_environment_1000m_10pcnt                                              0.08426
## Age                                                                           0.27231
## Sex                                                                           0.38613
## BMI                                                                           0.22640
## EducationCollege or University Degree                                         0.56854
## EducationCSEs or equivalent                                                   1.18159
## EducationNational Vocational Qualification or equivalent                      1.02491
## EducationNone of the above                                                    1.11431
## EducationO levels/General Certificate of Secondary Education or equivalent    0.66760
## EducationOther professional qualifications                                    1.04308
## Income                                                                        0.18495
##                                                                            t value
## (Intercept)                                                                 33.698
## Natural_environment_1000m_10pcnt                                            -1.497
## Age                                                                         15.300
## Sex                                                                         -0.170
## BMI                                                                          0.847
## EducationCollege or University Degree                                       -1.175
## EducationCSEs or equivalent                                                  3.605
## EducationNational Vocational Qualification or equivalent                     7.296
## EducationNone of the above                                                   9.106
## EducationO levels/General Certificate of Secondary Education or equivalent   2.399
## EducationOther professional qualifications                                   3.354
## Income                                                                      -5.573
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.134348
## Age                                                                         < 2e-16
## Sex                                                                        0.865208
## BMI                                                                        0.397139
## EducationCollege or University Degree                                      0.239906
## EducationCSEs or equivalent                                                0.000314
## EducationNational Vocational Qualification or equivalent                   3.21e-13
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.016474
## EducationOther professional qualifications                                 0.000801
## Income                                                                     2.58e-08
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.87 on 9156 degrees of freedom
## Multiple R-squared:  0.07043,    Adjusted R-squared:  0.06932 
## F-statistic: 63.07 on 11 and 9156 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                 2.5 %
## (Intercept)                                                                26.6859797
## Natural_environment_1000m_10pcnt                                           -0.2913440
## Age                                                                         3.6325558
## Sex                                                                        -0.8224403
## BMI                                                                        -0.2520879
## EducationCollege or University Degree                                      -1.7826836
## EducationCSEs or equivalent                                                 1.9433459
## EducationNational Vocational Qualification or equivalent                    5.4687750
## EducationNone of the above                                                  7.9621207
## EducationO levels/General Certificate of Secondary Education or equivalent  0.2927194
## EducationOther professional qualifications                                  1.4534724
## Income                                                                     -1.3932412
##                                                                                 97.5 %
## (Intercept)                                                                29.98243281
## Natural_environment_1000m_10pcnt                                            0.03900692
## Age                                                                         4.70013654
## Sex                                                                         0.69134829
## BMI                                                                         0.63551793
## EducationCollege or University Degree                                       0.44626398
## EducationCSEs or equivalent                                                 6.57569238
## EducationNational Vocational Qualification or equivalent                    9.48688398
## EducationNone of the above                                                 12.33069822
## EducationO levels/General Certificate of Secondary Education or equivalent  2.91000591
## EducationOther professional qualifications                                  5.54281992
## Income                                                                     -0.66813938

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Trails_B_A~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.927, -10.378, -2.474, 7.028, 175.881
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.663464
## Natural_environment_1000m_10pcnt                                           -0.166933
## Age                                                                         4.077772
## Sex                                                                         0.071358
## BMI                                                                         0.217272
## EducationCollege or University Degree                                      -0.584442
## EducationCSEs or equivalent                                                 3.946311
## EducationNational Vocational Qualification or equivalent                    7.233810
## EducationNone of the above                                                  9.687225
## EducationO levels/General Certificate of Secondary Education or equivalent  1.457983
## EducationOther professional qualifications                                  3.412258
## Income                                                                     -0.955003
## Average_time_outdoors                                                       0.236239
## Summed_PA_min                                                               0.002844
## Smoking                                                                     0.820508
## Disability                                                                 -0.151050
## Deprivation_Index                                                          -0.037015
## Population_density                                                          0.211265
##                                                                            Std. Error
## (Intercept)                                                                  1.078580
## Natural_environment_1000m_10pcnt                                             0.113990
## Age                                                                          0.274398
## Sex                                                                          0.389934
## BMI                                                                          0.228838
## EducationCollege or University Degree                                        0.569009
## EducationCSEs or equivalent                                                  1.184442
## EducationNational Vocational Qualification or equivalent                     1.026454
## EducationNone of the above                                                   1.121473
## EducationO levels/General Certificate of Secondary Education or equivalent   0.668308
## EducationOther professional qualifications                                   1.042621
## Income                                                                       0.187506
## Average_time_outdoors                                                        0.131406
## Summed_PA_min                                                                0.002256
## Smoking                                                                      0.316137
## Disability                                                                   0.449637
## Deprivation_Index                                                            0.013037
## Population_density                                                           0.415530
##                                                                            t value
## (Intercept)                                                                 24.721
## Natural_environment_1000m_10pcnt                                            -1.464
## Age                                                                         14.861
## Sex                                                                          0.183
## BMI                                                                          0.949
## EducationCollege or University Degree                                       -1.027
## EducationCSEs or equivalent                                                  3.332
## EducationNational Vocational Qualification or equivalent                     7.047
## EducationNone of the above                                                   8.638
## EducationO levels/General Certificate of Secondary Education or equivalent   2.182
## EducationOther professional qualifications                                   3.273
## Income                                                                      -5.093
## Average_time_outdoors                                                        1.798
## Summed_PA_min                                                                1.261
## Smoking                                                                      2.595
## Disability                                                                  -0.336
## Deprivation_Index                                                           -2.839
## Population_density                                                           0.508
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.143104
## Age                                                                         < 2e-16
## Sex                                                                        0.854801
## BMI                                                                        0.342414
## EducationCollege or University Degree                                      0.304390
## EducationCSEs or equivalent                                                0.000866
## EducationNational Vocational Qualification or equivalent                   1.96e-12
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.029164
## EducationOther professional qualifications                                 0.001069
## Income                                                                     3.59e-07
## Average_time_outdoors                                                      0.072246
## Summed_PA_min                                                              0.207329
## Smoking                                                                    0.009463
## Disability                                                                 0.736925
## Deprivation_Index                                                          0.004533
## Population_density                                                         0.611169
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ** 
## Income                                                                     ***
## Average_time_outdoors                                                      .  
## Summed_PA_min                                                                 
## Smoking                                                                    ** 
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.85 on 9150 degrees of freedom
## Multiple R-squared:  0.07277,    Adjusted R-squared:  0.07104 
## F-statistic: 42.24 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                24.549206807
## Natural_environment_1000m_10pcnt                                           -0.390379139
## Age                                                                         3.539890838
## Sex                                                                        -0.692999113
## BMI                                                                        -0.231301952
## EducationCollege or University Degree                                      -1.699827266
## EducationCSEs or equivalent                                                 1.624540408
## EducationNational Vocational Qualification or equivalent                    5.221731091
## EducationNone of the above                                                  7.488888807
## EducationO levels/General Certificate of Secondary Education or equivalent  0.147950357
## EducationOther professional qualifications                                  1.368489279
## Income                                                                     -1.322556339
## Average_time_outdoors                                                      -0.021346644
## Summed_PA_min                                                              -0.001577034
## Smoking                                                                     0.200809493
## Disability                                                                 -1.032439499
## Deprivation_Index                                                          -0.062571668
## Population_density                                                         -0.603266839
##                                                                                  97.5 %
## (Intercept)                                                                28.777720389
## Natural_environment_1000m_10pcnt                                            0.056512626
## Age                                                                         4.615652966
## Sex                                                                         0.835715815
## BMI                                                                         0.665845157
## EducationCollege or University Degree                                       0.530943196
## EducationCSEs or equivalent                                                 6.268081797
## EducationNational Vocational Qualification or equivalent                    9.245888988
## EducationNone of the above                                                 11.885562177
## EducationO levels/General Certificate of Secondary Education or equivalent  2.768014901
## EducationOther professional qualifications                                  5.456027478
## Income                                                                     -0.587449966
## Average_time_outdoors                                                       0.493824640
## Summed_PA_min                                                               0.007265585
## Smoking                                                                     1.440207490
## Disability                                                                  0.730339225
## Deprivation_Index                                                          -0.011459120
## Population_density                                                          1.025797540

Association of natural environment with Symbol Digit Substitution (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Symbol.Digit~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.3032, -2.4748, 0.2909, 2.7957, 17.5087
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                19.2587015
## Natural_environment_1000m_10pcnt                                            0.0763465
## Age                                                                        -2.3665938
## Sex                                                                         0.0276721
## BMI                                                                        -0.0004921
## EducationCollege or University Degree                                       0.2925091
## EducationCSEs or equivalent                                                -1.4101328
## EducationNational Vocational Qualification or equivalent                   -1.0763133
## EducationNone of the above                                                 -1.4857498
## EducationO levels/General Certificate of Secondary Education or equivalent -0.3501182
## EducationOther professional qualifications                                 -1.0872918
## Income                                                                      0.3692304
##                                                                            Std. Error
## (Intercept)                                                                 0.2017378
## Natural_environment_1000m_10pcnt                                            0.0202170
## Age                                                                         0.0653343
## Sex                                                                         0.0926415
## BMI                                                                         0.0543201
## EducationCollege or University Degree                                       0.1364082
## EducationCSEs or equivalent                                                 0.2834924
## EducationNational Vocational Qualification or equivalent                    0.2459021
## EducationNone of the above                                                  0.2673502
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1601739
## EducationOther professional qualifications                                  0.2502617
## Income                                                                      0.0443751
##                                                                            t value
## (Intercept)                                                                 95.464
## Natural_environment_1000m_10pcnt                                             3.776
## Age                                                                        -36.223
## Sex                                                                          0.299
## BMI                                                                         -0.009
## EducationCollege or University Degree                                        2.144
## EducationCSEs or equivalent                                                 -4.974
## EducationNational Vocational Qualification or equivalent                    -4.377
## EducationNone of the above                                                  -5.557
## EducationO levels/General Certificate of Secondary Education or equivalent  -2.186
## EducationOther professional qualifications                                  -4.345
## Income                                                                       8.321
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00016
## Age                                                                         < 2e-16
## Sex                                                                         0.76518
## BMI                                                                         0.99277
## EducationCollege or University Degree                                       0.03203
## EducationCSEs or equivalent                                                6.67e-07
## EducationNational Vocational Qualification or equivalent                   1.22e-05
## EducationNone of the above                                                 2.82e-08
## EducationO levels/General Certificate of Secondary Education or equivalent  0.02885
## EducationOther professional qualifications                                 1.41e-05
## Income                                                                      < 2e-16
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.287 on 9156 degrees of freedom
## Multiple R-squared:  0.1895, Adjusted R-squared:  0.1885 
## F-statistic: 194.6 on 11 and 9156 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                18.86325035
## Natural_environment_1000m_10pcnt                                            0.03671678
## Age                                                                        -2.49466361
## Sex                                                                        -0.15392595
## BMI                                                                        -0.10697165
## EducationCollege or University Degree                                       0.02511871
## EducationCSEs or equivalent                                                -1.96584122
## EducationNational Vocational Qualification or equivalent                   -1.55833620
## EducationNone of the above                                                 -2.00981588
## EducationO levels/General Certificate of Secondary Education or equivalent -0.66409481
## EducationOther professional qualifications                                 -1.57786066
## Income                                                                      0.28224526
##                                                                                 97.5 %
## (Intercept)                                                                19.65415270
## Natural_environment_1000m_10pcnt                                            0.11597630
## Age                                                                        -2.23852402
## Sex                                                                         0.20927017
## BMI                                                                         0.10598740
## EducationCollege or University Degree                                       0.55989953
## EducationCSEs or equivalent                                                -0.85442432
## EducationNational Vocational Qualification or equivalent                   -0.59429038
## EducationNone of the above                                                 -0.96168381
## EducationO levels/General Certificate of Secondary Education or equivalent -0.03614168
## EducationOther professional qualifications                                 -0.59672292
## Income                                                                      0.45621550

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Symbol.Digit~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.7309, -2.4487, 0.3098, 2.7826, 16.7792
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.4731781
## Natural_environment_1000m_10pcnt                                            0.1049642
## Age                                                                        -2.3017839
## Sex                                                                        -0.0647237
## BMI                                                                        -0.0003595
## EducationCollege or University Degree                                       0.2575920
## EducationCSEs or equivalent                                                -1.2375398
## EducationNational Vocational Qualification or equivalent                   -0.9552446
## EducationNone of the above                                                 -1.2323779
## EducationO levels/General Certificate of Secondary Education or equivalent -0.2744497
## EducationOther professional qualifications                                 -1.0226342
## Income                                                                      0.3158093
## Average_time_outdoors                                                      -0.1683762
## Summed_PA_min                                                              -0.0017416
## Smoking                                                                    -0.2049351
## Disability                                                                 -0.3315875
## Deprivation_Index                                                          -0.0035700
## Population_density                                                         -0.1259416
##                                                                            Std. Error
## (Intercept)                                                                 0.2579946
## Natural_environment_1000m_10pcnt                                            0.0272662
## Age                                                                         0.0656356
## Sex                                                                         0.0932716
## BMI                                                                         0.0547377
## EducationCollege or University Degree                                       0.1361062
## EducationCSEs or equivalent                                                 0.2833167
## EducationNational Vocational Qualification or equivalent                    0.2455262
## EducationNone of the above                                                  0.2682545
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1598582
## EducationOther professional qualifications                                  0.2493933
## Income                                                                      0.0448511
## Average_time_outdoors                                                       0.0314322
## Summed_PA_min                                                               0.0005395
## Smoking                                                                     0.0756195
## Disability                                                                  0.1075525
## Deprivation_Index                                                           0.0031185
## Population_density                                                          0.0993942
##                                                                            t value
## (Intercept)                                                                 79.355
## Natural_environment_1000m_10pcnt                                             3.850
## Age                                                                        -35.069
## Sex                                                                         -0.694
## BMI                                                                         -0.007
## EducationCollege or University Degree                                        1.893
## EducationCSEs or equivalent                                                 -4.368
## EducationNational Vocational Qualification or equivalent                    -3.891
## EducationNone of the above                                                  -4.594
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.717
## EducationOther professional qualifications                                  -4.100
## Income                                                                       7.041
## Average_time_outdoors                                                       -5.357
## Summed_PA_min                                                               -3.228
## Smoking                                                                     -2.710
## Disability                                                                  -3.083
## Deprivation_Index                                                           -1.145
## Population_density                                                          -1.267
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.000119
## Age                                                                         < 2e-16
## Sex                                                                        0.487746
## BMI                                                                        0.994760
## EducationCollege or University Degree                                      0.058445
## EducationCSEs or equivalent                                                1.27e-05
## EducationNational Vocational Qualification or equivalent                   0.000101
## EducationNone of the above                                                 4.41e-06
## EducationO levels/General Certificate of Secondary Education or equivalent 0.086044
## EducationOther professional qualifications                                 4.16e-05
## Income                                                                     2.04e-12
## Average_time_outdoors                                                      8.68e-08
## Summed_PA_min                                                              0.001251
## Smoking                                                                    0.006739
## Disability                                                                 0.002055
## Deprivation_Index                                                          0.252333
## Population_density                                                         0.205155
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    ** 
## Disability                                                                 ** 
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.27 on 9150 degrees of freedom
## Multiple R-squared:  0.1964, Adjusted R-squared:  0.1949 
## F-statistic: 131.5 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                19.967451090
## Natural_environment_1000m_10pcnt                                            0.051516251
## Age                                                                        -2.430444220
## Sex                                                                        -0.247556801
## BMI                                                                        -0.107657594
## EducationCollege or University Degree                                      -0.009206467
## EducationCSEs or equivalent                                                -1.792903879
## EducationNational Vocational Qualification or equivalent                   -1.436530833
## EducationNone of the above                                                 -1.758216755
## EducationO levels/General Certificate of Secondary Education or equivalent -0.587807474
## EducationOther professional qualifications                                 -1.511500698
## Income                                                                      0.227891155
## Average_time_outdoors                                                      -0.229990279
## Summed_PA_min                                                              -0.002799142
## Smoking                                                                    -0.353166119
## Disability                                                                 -0.542414459
## Deprivation_Index                                                          -0.009683033
## Population_density                                                         -0.320776479
##                                                                                   97.5 %
## (Intercept)                                                                20.9789051429
## Natural_environment_1000m_10pcnt                                            0.1584120858
## Age                                                                        -2.1731235461
## Sex                                                                         0.1181094974
## BMI                                                                         0.1069386373
## EducationCollege or University Degree                                       0.5243904535
## EducationCSEs or equivalent                                                -0.6821758025
## EducationNational Vocational Qualification or equivalent                   -0.4739583508
## EducationNone of the above                                                 -0.7065391351
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0389080015
## EducationOther professional qualifications                                 -0.5337677439
## Income                                                                      0.4037274876
## Average_time_outdoors                                                      -0.1067620869
## Summed_PA_min                                                              -0.0006840011
## Smoking                                                                    -0.0567039925
## Disability                                                                 -0.1207604545
## Deprivation_Index                                                           0.0025430109
## Population_density                                                          0.0688932561

Moderation by sex: association of natural environment with TMT (B-A) (not significant)

summary_confint(lm(Trails_B_A~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.538, -10.381, -2.423, 7.011, 176.088
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.662969
## Natural_environment_1000m_10pcnt                                           -0.169454
## Sex                                                                        -1.122815
## Age                                                                         4.081136
## BMI                                                                         0.215167
## EducationCollege or University Degree                                      -0.583652
## EducationCSEs or equivalent                                                 3.961498
## EducationNational Vocational Qualification or equivalent                    7.244276
## EducationNone of the above                                                  9.663189
## EducationO levels/General Certificate of Secondary Education or equivalent  1.446051
## EducationOther professional qualifications                                  3.408938
## Income                                                                     -0.952674
## Average_time_outdoors                                                       0.239930
## Summed_PA_min                                                               0.002838
## Smoking                                                                     0.822732
## Disability                                                                 -0.148156
## Deprivation_Index                                                          -0.037013
## Population_density                                                          0.214798
## Natural_environment_1000m_10pcnt:Sex                                        0.250516
##                                                                            Std. Error
## (Intercept)                                                                  1.078507
## Natural_environment_1000m_10pcnt                                             0.113995
## Sex                                                                          0.890580
## Age                                                                          0.274389
## BMI                                                                          0.228827
## EducationCollege or University Degree                                        0.568971
## EducationCSEs or equivalent                                                  1.184406
## EducationNational Vocational Qualification or equivalent                     1.026409
## EducationNone of the above                                                   1.121513
## EducationO levels/General Certificate of Secondary Education or equivalent   0.668311
## EducationOther professional qualifications                                   1.042553
## Income                                                                       0.187500
## Average_time_outdoors                                                        0.131421
## Summed_PA_min                                                                0.002255
## Smoking                                                                      0.316119
## Disability                                                                   0.449611
## Deprivation_Index                                                            0.013037
## Population_density                                                           0.415509
## Natural_environment_1000m_10pcnt:Sex                                         0.167970
##                                                                            t value
## (Intercept)                                                                 24.722
## Natural_environment_1000m_10pcnt                                            -1.487
## Sex                                                                         -1.261
## Age                                                                         14.874
## BMI                                                                          0.940
## EducationCollege or University Degree                                       -1.026
## EducationCSEs or equivalent                                                  3.345
## EducationNational Vocational Qualification or equivalent                     7.058
## EducationNone of the above                                                   8.616
## EducationO levels/General Certificate of Secondary Education or equivalent   2.164
## EducationOther professional qualifications                                   3.270
## Income                                                                      -5.081
## Average_time_outdoors                                                        1.826
## Summed_PA_min                                                                1.258
## Smoking                                                                      2.603
## Disability                                                                  -0.330
## Deprivation_Index                                                           -2.839
## Population_density                                                           0.517
## Natural_environment_1000m_10pcnt:Sex                                         1.491
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.137179
## Sex                                                                        0.207424
## Age                                                                         < 2e-16
## BMI                                                                        0.347087
## EducationCollege or University Degree                                      0.305012
## EducationCSEs or equivalent                                                0.000827
## EducationNational Vocational Qualification or equivalent                   1.81e-12
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.030510
## EducationOther professional qualifications                                 0.001080
## Income                                                                     3.83e-07
## Average_time_outdoors                                                      0.067934
## Summed_PA_min                                                              0.208311
## Smoking                                                                    0.009267
## Disability                                                                 0.741771
## Deprivation_Index                                                          0.004533
## Population_density                                                         0.605203
## Natural_environment_1000m_10pcnt:Sex                                       0.135883
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ** 
## Income                                                                     ***
## Average_time_outdoors                                                      .  
## Summed_PA_min                                                                 
## Smoking                                                                    ** 
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.85 on 9149 degrees of freedom
## Multiple R-squared:  0.07299,    Adjusted R-squared:  0.07117 
## F-statistic: 40.02 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                24.548853871
## Natural_environment_1000m_10pcnt                                           -0.392909997
## Sex                                                                        -2.868550465
## Age                                                                         3.543273190
## BMI                                                                        -0.233385201
## EducationCollege or University Degree                                      -1.698962889
## EducationCSEs or equivalent                                                 1.639796938
## EducationNational Vocational Qualification or equivalent                    5.232284368
## EducationNone of the above                                                  7.464772170
## EducationO levels/General Certificate of Secondary Education or equivalent  0.136012330
## EducationOther professional qualifications                                  1.365300878
## Income                                                                     -1.320215325
## Average_time_outdoors                                                      -0.017684099
## Summed_PA_min                                                              -0.001583066
## Smoking                                                                     0.203067599
## Disability                                                                 -1.029494161
## Deprivation_Index                                                          -0.062567346
## Population_density                                                         -0.599693275
## Natural_environment_1000m_10pcnt:Sex                                       -0.078743281
##                                                                                  97.5 %
## (Intercept)                                                                28.777084833
## Natural_environment_1000m_10pcnt                                            0.054001022
## Sex                                                                         0.622920449
## Age                                                                         4.618999725
## BMI                                                                         0.663718964
## EducationCollege or University Degree                                       0.531659337
## EducationCSEs or equivalent                                                 6.283199363
## EducationNational Vocational Qualification or equivalent                    9.256267155
## EducationNone of the above                                                 11.861605484
## EducationO levels/General Certificate of Secondary Education or equivalent  2.756089369
## EducationOther professional qualifications                                  5.452575005
## Income                                                                     -0.585132621
## Average_time_outdoors                                                       0.497544090
## Summed_PA_min                                                               0.007258978
## Smoking                                                                     1.442396483
## Disability                                                                  0.733183085
## Deprivation_Index                                                          -0.011458216
## Population_density                                                          1.029288610
## Natural_environment_1000m_10pcnt:Sex                                        0.579775228

Moderation by sex: association of natural environment with Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Natural_environment_1000m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.7293, -2.4524, 0.3082, 2.7814, 16.7602
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.4731211
## Natural_environment_1000m_10pcnt                                            0.1046734
## Sex                                                                        -0.2024285
## Age                                                                        -2.3013959
## BMI                                                                        -0.0006022
## EducationCollege or University Degree                                       0.2576831
## EducationCSEs or equivalent                                                -1.2357886
## EducationNational Vocational Qualification or equivalent                   -0.9540377
## EducationNone of the above                                                 -1.2351497
## EducationO levels/General Certificate of Secondary Education or equivalent -0.2758256
## EducationOther professional qualifications                                 -1.0230171
## Income                                                                      0.3160779
## Average_time_outdoors                                                      -0.1679506
## Summed_PA_min                                                              -0.0017423
## Smoking                                                                    -0.2046786
## Disability                                                                 -0.3312537
## Deprivation_Index                                                          -0.0035697
## Population_density                                                         -0.1255343
## Natural_environment_1000m_10pcnt:Sex                                        0.0288880
##                                                                            Std. Error
## (Intercept)                                                                 0.2580014
## Natural_environment_1000m_10pcnt                                            0.0272700
## Sex                                                                         0.2130452
## Age                                                                         0.0656395
## BMI                                                                         0.0547402
## EducationCollege or University Degree                                       0.1361098
## EducationCSEs or equivalent                                                 0.2833347
## EducationNational Vocational Qualification or equivalent                    0.2455385
## EducationNone of the above                                                  0.2682893
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1598739
## EducationOther professional qualifications                                  0.2494004
## Income                                                                      0.0448538
## Average_time_outdoors                                                       0.0314386
## Summed_PA_min                                                               0.0005395
## Smoking                                                                     0.0756223
## Disability                                                                  0.1075564
## Deprivation_Index                                                           0.0031186
## Population_density                                                          0.0993985
## Natural_environment_1000m_10pcnt:Sex                                        0.0401820
##                                                                            t value
## (Intercept)                                                                 79.353
## Natural_environment_1000m_10pcnt                                             3.838
## Sex                                                                         -0.950
## Age                                                                        -35.061
## BMI                                                                         -0.011
## EducationCollege or University Degree                                        1.893
## EducationCSEs or equivalent                                                 -4.362
## EducationNational Vocational Qualification or equivalent                    -3.885
## EducationNone of the above                                                  -4.604
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.725
## EducationOther professional qualifications                                  -4.102
## Income                                                                       7.047
## Average_time_outdoors                                                       -5.342
## Summed_PA_min                                                               -3.229
## Smoking                                                                     -2.707
## Disability                                                                  -3.080
## Deprivation_Index                                                           -1.145
## Population_density                                                          -1.263
## Natural_environment_1000m_10pcnt:Sex                                         0.719
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                           0.000125
## Sex                                                                        0.342053
## Age                                                                         < 2e-16
## BMI                                                                        0.991223
## EducationCollege or University Degree                                      0.058363
## EducationCSEs or equivalent                                                1.31e-05
## EducationNational Vocational Qualification or equivalent                   0.000103
## EducationNone of the above                                                 4.20e-06
## EducationO levels/General Certificate of Secondary Education or equivalent 0.084513
## EducationOther professional qualifications                                 4.13e-05
## Income                                                                     1.96e-12
## Average_time_outdoors                                                      9.40e-08
## Summed_PA_min                                                              0.001245
## Smoking                                                                    0.006810
## Disability                                                                 0.002077
## Deprivation_Index                                                          0.252386
## Population_density                                                         0.206643
## Natural_environment_1000m_10pcnt:Sex                                       0.472203
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ***
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    ** 
## Disability                                                                 ** 
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.27 on 9149 degrees of freedom
## Multiple R-squared:  0.1964, Adjusted R-squared:  0.1949 
## F-statistic: 124.3 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                19.967380713
## Natural_environment_1000m_10pcnt                                            0.051218228
## Sex                                                                        -0.620044705
## Age                                                                        -2.430063987
## BMI                                                                        -0.107905173
## EducationCollege or University Degree                                      -0.009122503
## EducationCSEs or equivalent                                                -1.791187799
## EducationNational Vocational Qualification or equivalent                   -1.435347952
## EducationNone of the above                                                 -1.761056712
## EducationO levels/General Certificate of Secondary Education or equivalent -0.589214108
## EducationOther professional qualifications                                 -1.511897620
## Income                                                                      0.228154370
## Average_time_outdoors                                                      -0.229577211
## Summed_PA_min                                                              -0.002799901
## Smoking                                                                    -0.352915277
## Disability                                                                 -0.542088205
## Deprivation_Index                                                          -0.009682894
## Population_density                                                         -0.320377466
## Natural_environment_1000m_10pcnt:Sex                                       -0.049877686
##                                                                                  97.5 %
## (Intercept)                                                                20.978861533
## Natural_environment_1000m_10pcnt                                            0.158128643
## Sex                                                                         0.215187783
## Age                                                                        -2.172727818
## BMI                                                                         0.106700809
## EducationCollege or University Degree                                       0.524488745
## EducationCSEs or equivalent                                                -0.680389327
## EducationNational Vocational Qualification or equivalent                   -0.472727545
## EducationNone of the above                                                 -0.709242702
## EducationO levels/General Certificate of Secondary Education or equivalent  0.037562834
## EducationOther professional qualifications                                 -0.534136608
## Income                                                                      0.404001447
## Average_time_outdoors                                                      -0.106323908
## Summed_PA_min                                                              -0.000684700
## Smoking                                                                    -0.056442022
## Disability                                                                 -0.120419133
## Deprivation_Index                                                           0.002543474
## Population_density                                                          0.069308894
## Natural_environment_1000m_10pcnt:Sex                                        0.107653643

9.2.2) 300m natural environment buffer

Association of natural environment (300m buffer) with Trail-making Test (B-A)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Age + 
##     Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.734, -10.406, -2.452, 6.989, 175.803
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.381755
## Natural_environment_300m_10pcnt                                            -0.112072
## Age                                                                         4.073158
## Sex                                                                         0.089566
## BMI                                                                         0.214924
## EducationCollege or University Degree                                      -0.559091
## EducationCSEs or equivalent                                                 3.933304
## EducationNational Vocational Qualification or equivalent                    7.232788
## EducationNone of the above                                                  9.689816
## EducationO levels/General Certificate of Secondary Education or equivalent  1.454420
## EducationOther professional qualifications                                  3.413046
## Income                                                                     -0.946401
## Average_time_outdoors                                                       0.237955
## Summed_PA_min                                                               0.002798
## Smoking                                                                     0.831207
## Disability                                                                 -0.143590
## Deprivation_Index                                                          -0.037113
## Population_density                                                          0.098042
##                                                                            Std. Error
## (Intercept)                                                                  1.055258
## Natural_environment_300m_10pcnt                                              0.102294
## Age                                                                          0.274379
## Sex                                                                          0.389667
## BMI                                                                          0.228839
## EducationCollege or University Degree                                        0.568590
## EducationCSEs or equivalent                                                  1.184457
## EducationNational Vocational Qualification or equivalent                     1.026608
## EducationNone of the above                                                   1.121595
## EducationO levels/General Certificate of Secondary Education or equivalent   0.668391
## EducationOther professional qualifications                                   1.042734
## Income                                                                       0.187471
## Average_time_outdoors                                                        0.131447
## Summed_PA_min                                                                0.002255
## Smoking                                                                      0.315965
## Disability                                                                   0.449643
## Deprivation_Index                                                            0.013038
## Population_density                                                           0.409265
##                                                                            t value
## (Intercept)                                                                 25.000
## Natural_environment_300m_10pcnt                                             -1.096
## Age                                                                         14.845
## Sex                                                                          0.230
## BMI                                                                          0.939
## EducationCollege or University Degree                                       -0.983
## EducationCSEs or equivalent                                                  3.321
## EducationNational Vocational Qualification or equivalent                     7.045
## EducationNone of the above                                                   8.639
## EducationO levels/General Certificate of Secondary Education or equivalent   2.176
## EducationOther professional qualifications                                   3.273
## Income                                                                      -5.048
## Average_time_outdoors                                                        1.810
## Summed_PA_min                                                                1.241
## Smoking                                                                      2.631
## Disability                                                                  -0.319
## Deprivation_Index                                                           -2.847
## Population_density                                                           0.240
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.273285
## Age                                                                         < 2e-16
## Sex                                                                        0.818212
## BMI                                                                        0.347657
## EducationCollege or University Degree                                      0.325489
## EducationCSEs or equivalent                                                0.000901
## EducationNational Vocational Qualification or equivalent                   1.98e-12
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent 0.029581
## EducationOther professional qualifications                                 0.001067
## Income                                                                     4.54e-07
## Average_time_outdoors                                                      0.070285
## Summed_PA_min                                                              0.214687
## Smoking                                                                    0.008535
## Disability                                                                 0.749474
## Deprivation_Index                                                          0.004430
## Population_density                                                         0.810679
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ** 
## Income                                                                     ***
## Average_time_outdoors                                                      .  
## Summed_PA_min                                                                 
## Smoking                                                                    ** 
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.85 on 9150 degrees of freedom
## Multiple R-squared:  0.07267,    Adjusted R-squared:  0.07095 
## F-statistic: 42.18 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                24.313214098
## Natural_environment_300m_10pcnt                                            -0.312590826
## Age                                                                         3.535313556
## Sex                                                                        -0.674268685
## BMI                                                                        -0.233651339
## EducationCollege or University Degree                                      -1.673654192
## EducationCSEs or equivalent                                                 1.611504515
## EducationNational Vocational Qualification or equivalent                    5.220407104
## EducationNone of the above                                                  7.491239712
## EducationO levels/General Certificate of Secondary Education or equivalent  0.144224256
## EducationOther professional qualifications                                  1.369055455
## Income                                                                     -1.313886331
## Average_time_outdoors                                                      -0.019709795
## Summed_PA_min                                                              -0.001622318
## Smoking                                                                     0.211845810
## Disability                                                                 -1.024989698
## Deprivation_Index                                                          -0.062671216
## Population_density                                                         -0.704208790
##                                                                                 97.5 %
## (Intercept)                                                                28.45029561
## Natural_environment_300m_10pcnt                                             0.08844608
## Age                                                                         4.61100308
## Sex                                                                         0.85339985
## BMI                                                                         0.66349840
## EducationCollege or University Degree                                       0.55547311
## EducationCSEs or equivalent                                                 6.25510345
## EducationNational Vocational Qualification or equivalent                    9.24516931
## EducationNone of the above                                                 11.88839162
## EducationO levels/General Certificate of Secondary Education or equivalent  2.76461534
## EducationOther professional qualifications                                  5.45703653
## Income                                                                     -0.57891609
## Average_time_outdoors                                                       0.49561962
## Summed_PA_min                                                               0.00721920
## Smoking                                                                     1.45056908
## Disability                                                                  0.73780996
## Deprivation_Index                                                          -0.01155550
## Population_density                                                          0.90029339

Association of natural environment (300m buffer) with Symbol Digit Substitution

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.6608, -2.4665, 0.3111, 2.7845, 16.8734
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.6583829
## Natural_environment_300m_10pcnt                                             0.0533742
## Age                                                                        -2.2985292
## Sex                                                                        -0.0768605
## BMI                                                                         0.0017894
## EducationCollege or University Degree                                       0.2400243
## EducationCSEs or equivalent                                                -1.2289340
## EducationNational Vocational Qualification or equivalent                   -0.9507641
## EducationNone of the above                                                 -1.2314128
## EducationO levels/General Certificate of Secondary Education or equivalent -0.2692843
## EducationOther professional qualifications                                 -1.0204769
## Income                                                                      0.3107112
## Average_time_outdoors                                                      -0.1689176
## Summed_PA_min                                                              -0.0017091
## Smoking                                                                    -0.2133681
## Disability                                                                 -0.3360756
## Deprivation_Index                                                          -0.0035189
## Population_density                                                         -0.0097173
##                                                                            Std. Error
## (Intercept)                                                                 0.2525418
## Natural_environment_300m_10pcnt                                             0.0244807
## Age                                                                         0.0656638
## Sex                                                                         0.0932542
## BMI                                                                         0.0547651
## EducationCollege or University Degree                                       0.1360736
## EducationCSEs or equivalent                                                 0.2834613
## EducationNational Vocational Qualification or equivalent                    0.2456854
## EducationNone of the above                                                  0.2684173
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1599577
## EducationOther professional qualifications                                  0.2495445
## Income                                                                      0.0448651
## Average_time_outdoors                                                       0.0314575
## Summed_PA_min                                                               0.0005397
## Smoking                                                                     0.0756159
## Disability                                                                  0.1076074
## Deprivation_Index                                                           0.0031203
## Population_density                                                          0.0979444
##                                                                            t value
## (Intercept)                                                                 81.802
## Natural_environment_300m_10pcnt                                              2.180
## Age                                                                        -35.005
## Sex                                                                         -0.824
## BMI                                                                          0.033
## EducationCollege or University Degree                                        1.764
## EducationCSEs or equivalent                                                 -4.335
## EducationNational Vocational Qualification or equivalent                    -3.870
## EducationNone of the above                                                  -4.588
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.683
## EducationOther professional qualifications                                  -4.089
## Income                                                                       6.925
## Average_time_outdoors                                                       -5.370
## Summed_PA_min                                                               -3.167
## Smoking                                                                     -2.822
## Disability                                                                  -3.123
## Deprivation_Index                                                           -1.128
## Population_density                                                          -0.099
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.02926
## Age                                                                         < 2e-16
## Sex                                                                         0.40984
## BMI                                                                         0.97394
## EducationCollege or University Degree                                       0.07778
## EducationCSEs or equivalent                                                1.47e-05
## EducationNational Vocational Qualification or equivalent                    0.00011
## EducationNone of the above                                                 4.54e-06
## EducationO levels/General Certificate of Secondary Education or equivalent  0.09232
## EducationOther professional qualifications                                 4.36e-05
## Income                                                                     4.64e-12
## Average_time_outdoors                                                      8.08e-08
## Summed_PA_min                                                               0.00155
## Smoking                                                                     0.00479
## Disability                                                                  0.00179
## Deprivation_Index                                                           0.25946
## Population_density                                                          0.92097
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Age                                                                        ***
## Sex                                                                           
## BMI                                                                           
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    ** 
## Disability                                                                 ** 
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.273 on 9150 degrees of freedom
## Multiple R-squared:  0.1955, Adjusted R-squared:  0.194 
## F-statistic: 130.8 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.163344718
## Natural_environment_300m_10pcnt                                             0.005386599
## Age                                                                        -2.427244959
## Sex                                                                        -0.259659503
## BMI                                                                        -0.105562489
## EducationCollege or University Degree                                      -0.026710424
## EducationCSEs or equivalent                                                -1.784581532
## EducationNational Vocational Qualification or equivalent                   -1.432362372
## EducationNone of the above                                                 -1.757570707
## EducationO levels/General Certificate of Secondary Education or equivalent -0.582837173
## EducationOther professional qualifications                                 -1.509639866
## Income                                                                      0.222765535
## Average_time_outdoors                                                      -0.230581328
## Summed_PA_min                                                              -0.002767065
## Smoking                                                                    -0.361592281
## Disability                                                                 -0.547010143
## Deprivation_Index                                                          -0.009635304
## Population_density                                                         -0.201710100
##                                                                                   97.5 %
## (Intercept)                                                                21.1534211640
## Natural_environment_300m_10pcnt                                             0.1013617919
## Age                                                                        -2.1698135152
## Sex                                                                         0.1059384759
## BMI                                                                         0.1091412388
## EducationCollege or University Degree                                       0.5067589881
## EducationCSEs or equivalent                                                -0.6732865479
## EducationNational Vocational Qualification or equivalent                   -0.4691659134
## EducationNone of the above                                                 -0.7052548349
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0442685511
## EducationOther professional qualifications                                 -0.5313140179
## Income                                                                      0.3986568551
## Average_time_outdoors                                                      -0.1072539242
## Summed_PA_min                                                              -0.0006511342
## Smoking                                                                    -0.0651439919
## Disability                                                                 -0.1251411489
## Deprivation_Index                                                           0.0025975861
## Population_density                                                          0.1822755210

Moderation by sex: association of natural environment (300m buffer) with TMT (B-A)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt * Sex + 
##     Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -134.285, -10.387, -2.448, 7.049, 176.402
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                26.368445
## Natural_environment_300m_10pcnt                                            -0.113747
## Sex                                                                        -1.249872
## Age                                                                         4.065600
## BMI                                                                         0.216172
## EducationCollege or University Degree                                      -0.559340
## EducationCSEs or equivalent                                                 3.940362
## EducationNational Vocational Qualification or equivalent                    7.252089
## EducationNone of the above                                                  9.663659
## EducationO levels/General Certificate of Secondary Education or equivalent  1.442596
## EducationOther professional qualifications                                  3.390594
## Income                                                                     -0.942762
## Average_time_outdoors                                                       0.246941
## Summed_PA_min                                                               0.002706
## Smoking                                                                     0.827869
## Disability                                                                 -0.135765
## Deprivation_Index                                                          -0.036921
## Population_density                                                          0.104181
## Natural_environment_300m_10pcnt:Sex                                         0.353851
##                                                                            Std. Error
## (Intercept)                                                                  1.055024
## Natural_environment_300m_10pcnt                                              0.102272
## Sex                                                                          0.698684
## Age                                                                          0.274334
## BMI                                                                          0.228785
## EducationCollege or University Degree                                        0.568456
## EducationCSEs or equivalent                                                  1.184180
## EducationNational Vocational Qualification or equivalent                     1.026399
## EducationNone of the above                                                   1.121386
## EducationO levels/General Certificate of Secondary Education or equivalent   0.668252
## EducationOther professional qualifications                                   1.042532
## Income                                                                       0.187433
## Average_time_outdoors                                                        0.131473
## Summed_PA_min                                                                0.002255
## Smoking                                                                      0.315893
## Disability                                                                   0.449549
## Deprivation_Index                                                            0.013035
## Population_density                                                           0.409177
## Natural_environment_300m_10pcnt:Sex                                          0.153222
##                                                                            t value
## (Intercept)                                                                 24.993
## Natural_environment_300m_10pcnt                                             -1.112
## Sex                                                                         -1.789
## Age                                                                         14.820
## BMI                                                                          0.945
## EducationCollege or University Degree                                       -0.984
## EducationCSEs or equivalent                                                  3.328
## EducationNational Vocational Qualification or equivalent                     7.066
## EducationNone of the above                                                   8.618
## EducationO levels/General Certificate of Secondary Education or equivalent   2.159
## EducationOther professional qualifications                                   3.252
## Income                                                                      -5.030
## Average_time_outdoors                                                        1.878
## Summed_PA_min                                                                1.200
## Smoking                                                                      2.621
## Disability                                                                  -0.302
## Deprivation_Index                                                           -2.832
## Population_density                                                           0.255
## Natural_environment_300m_10pcnt:Sex                                          2.309
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.26608
## Sex                                                                         0.07367
## Age                                                                         < 2e-16
## BMI                                                                         0.34475
## EducationCollege or University Degree                                       0.32516
## EducationCSEs or equivalent                                                 0.00088
## EducationNational Vocational Qualification or equivalent                   1.72e-12
## EducationNone of the above                                                  < 2e-16
## EducationO levels/General Certificate of Secondary Education or equivalent  0.03089
## EducationOther professional qualifications                                  0.00115
## Income                                                                     5.00e-07
## Average_time_outdoors                                                       0.06038
## Summed_PA_min                                                               0.23013
## Smoking                                                                     0.00879
## Disability                                                                  0.76266
## Deprivation_Index                                                           0.00463
## Population_density                                                          0.79903
## Natural_environment_300m_10pcnt:Sex                                         0.02094
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Sex                                                                        .  
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                 ** 
## Income                                                                     ***
## Average_time_outdoors                                                      .  
## Summed_PA_min                                                                 
## Smoking                                                                    ** 
## Disability                                                                    
## Deprivation_Index                                                          ** 
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                        *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.85 on 9149 degrees of freedom
## Multiple R-squared:  0.07321,    Adjusted R-squared:  0.07139 
## F-statistic: 40.15 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                24.300362655
## Natural_environment_300m_10pcnt                                            -0.314223488
## Sex                                                                        -2.619448954
## Age                                                                         3.527844438
## BMI                                                                        -0.232298112
## EducationCollege or University Degree                                      -1.673639924
## EducationCSEs or equivalent                                                 1.619104411
## EducationNational Vocational Qualification or equivalent                    5.240117575
## EducationNone of the above                                                  7.465490868
## EducationO levels/General Certificate of Secondary Education or equivalent  0.132671955
## EducationOther professional qualifications                                  1.346998494
## Income                                                                     -1.310173480
## Average_time_outdoors                                                      -0.010775323
## Summed_PA_min                                                              -0.001714116
## Smoking                                                                     0.208647807
## Disability                                                                 -1.016981293
## Deprivation_Index                                                          -0.062473344
## Population_density                                                         -0.697897157
## Natural_environment_300m_10pcnt:Sex                                         0.053502038
##                                                                                  97.5 %
## (Intercept)                                                                28.436526650
## Natural_environment_300m_10pcnt                                             0.086728581
## Sex                                                                         0.119705869
## Age                                                                         4.603355892
## BMI                                                                         0.664641774
## EducationCollege or University Degree                                       0.554959795
## EducationCSEs or equivalent                                                 6.261619681
## EducationNational Vocational Qualification or equivalent                    9.264060528
## EducationNone of the above                                                 11.861826243
## EducationO levels/General Certificate of Secondary Education or equivalent  2.752519699
## EducationOther professional qualifications                                  5.434189679
## Income                                                                     -0.575351234
## Average_time_outdoors                                                       0.504657926
## Summed_PA_min                                                               0.007126692
## Smoking                                                                     1.447090842
## Disability                                                                  0.745451172
## Deprivation_Index                                                          -0.011368688
## Population_density                                                          0.906259089
## Natural_environment_300m_10pcnt:Sex                                         0.654199467

Moderation by sex: association of natural environment (300m buffer) with Symbol Digit Substitution

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt*Sex + Age + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -22.658, -2.4634, 0.311, 2.7799, 16.8683
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                20.6580619
## Natural_environment_300m_10pcnt                                             0.0533338
## Sex                                                                        -0.1091690
## Age                                                                        -2.2987115
## BMI                                                                         0.0018195
## EducationCollege or University Degree                                       0.2400183
## EducationCSEs or equivalent                                                -1.2287638
## EducationNational Vocational Qualification or equivalent                   -0.9502986
## EducationNone of the above                                                 -1.2320437
## EducationO levels/General Certificate of Secondary Education or equivalent -0.2695695
## EducationOther professional qualifications                                 -1.0210185
## Income                                                                      0.3107990
## Average_time_outdoors                                                      -0.1687009
## Summed_PA_min                                                              -0.0017113
## Smoking                                                                    -0.2134487
## Disability                                                                 -0.3358869
## Deprivation_Index                                                          -0.0035142
## Population_density                                                         -0.0095692
## Natural_environment_300m_10pcnt:Sex                                         0.0085352
##                                                                            Std. Error
## (Intercept)                                                                 0.2525586
## Natural_environment_300m_10pcnt                                             0.0244826
## Sex                                                                         0.1672557
## Age                                                                         0.0656719
## BMI                                                                         0.0547681
## EducationCollege or University Degree                                       0.1360807
## EducationCSEs or equivalent                                                 0.2834769
## EducationNational Vocational Qualification or equivalent                    0.2457062
## EducationNone of the above                                                  0.2684449
## EducationO levels/General Certificate of Secondary Education or equivalent  0.1599707
## EducationOther professional qualifications                                  0.2495682
## Income                                                                      0.0448690
## Average_time_outdoors                                                       0.0314729
## Summed_PA_min                                                               0.0005398
## Smoking                                                                     0.0756206
## Disability                                                                  0.1076160
## Deprivation_Index                                                           0.0031205
## Population_density                                                          0.0979515
## Natural_environment_300m_10pcnt:Sex                                         0.0366792
##                                                                            t value
## (Intercept)                                                                 81.795
## Natural_environment_300m_10pcnt                                              2.178
## Sex                                                                         -0.653
## Age                                                                        -35.003
## BMI                                                                          0.033
## EducationCollege or University Degree                                        1.764
## EducationCSEs or equivalent                                                 -4.335
## EducationNational Vocational Qualification or equivalent                    -3.868
## EducationNone of the above                                                  -4.590
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.685
## EducationOther professional qualifications                                  -4.091
## Income                                                                       6.927
## Average_time_outdoors                                                       -5.360
## Summed_PA_min                                                               -3.170
## Smoking                                                                     -2.823
## Disability                                                                  -3.121
## Deprivation_Index                                                           -1.126
## Population_density                                                          -0.098
## Natural_environment_300m_10pcnt:Sex                                          0.233
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                            0.029399
## Sex                                                                        0.513962
## Age                                                                         < 2e-16
## BMI                                                                        0.973499
## EducationCollege or University Degree                                      0.077800
## EducationCSEs or equivalent                                                1.48e-05
## EducationNational Vocational Qualification or equivalent                   0.000111
## EducationNone of the above                                                 4.50e-06
## EducationO levels/General Certificate of Secondary Education or equivalent 0.092000
## EducationOther professional qualifications                                 4.33e-05
## Income                                                                     4.59e-12
## Average_time_outdoors                                                      8.52e-08
## Summed_PA_min                                                              0.001529
## Smoking                                                                    0.004774
## Disability                                                                 0.001807
## Deprivation_Index                                                          0.260123
## Population_density                                                         0.922178
## Natural_environment_300m_10pcnt:Sex                                        0.816001
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Sex                                                                           
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                ***
## EducationNational Vocational Qualification or equivalent                   ***
## EducationNone of the above                                                 ***
## EducationO levels/General Certificate of Secondary Education or equivalent .  
## EducationOther professional qualifications                                 ***
## Income                                                                     ***
## Average_time_outdoors                                                      ***
## Summed_PA_min                                                              ** 
## Smoking                                                                    ** 
## Disability                                                                 ** 
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.273 on 9149 degrees of freedom
## Multiple R-squared:  0.1955, Adjusted R-squared:  0.1939 
## F-statistic: 123.5 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                20.162990681
## Natural_environment_300m_10pcnt                                             0.005342506
## Sex                                                                        -0.437027507
## Age                                                                        -2.427443085
## BMI                                                                        -0.105538229
## EducationCollege or University Degree                                      -0.026730239
## EducationCSEs or equivalent                                                -1.784441865
## EducationNational Vocational Qualification or equivalent                   -1.431937685
## EducationNone of the above                                                 -1.758255687
## EducationO levels/General Certificate of Secondary Education or equivalent -0.583147794
## EducationOther professional qualifications                                 -1.510227990
## Income                                                                      0.222845652
## Average_time_outdoors                                                      -0.230394784
## Summed_PA_min                                                              -0.002769508
## Smoking                                                                    -0.361682015
## Disability                                                                 -0.546838300
## Deprivation_Index                                                          -0.009631105
## Population_density                                                         -0.201576008
## Natural_environment_300m_10pcnt:Sex                                        -0.063364265
##                                                                                   97.5 %
## (Intercept)                                                                21.1531330927
## Natural_environment_300m_10pcnt                                             0.1013250755
## Sex                                                                         0.2186895697
## Age                                                                        -2.1699800086
## BMI                                                                         0.1091771992
## EducationCollege or University Degree                                       0.5067667654
## EducationCSEs or equivalent                                                -0.6730857208
## EducationNational Vocational Qualification or equivalent                   -0.4686594917
## EducationNone of the above                                                 -0.7058317221
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0440087619
## EducationOther professional qualifications                                 -0.5318090150
## Income                                                                      0.3987522826
## Average_time_outdoors                                                      -0.1070069486
## Summed_PA_min                                                              -0.0006531366
## Smoking                                                                    -0.0652152948
## Disability                                                                 -0.1249355093
## Deprivation_Index                                                           0.0026026667
## Population_density                                                          0.1824375697
## Natural_environment_300m_10pcnt:Sex                                         0.0804346759

10) Sensitivity analyses for brain volumes

10.1) Greenspace percentage instead of natural environment percentage

10.1.1) 1000m greenspace buffer

Association of greenspace (buffered to 1000m) with grey matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -169.882, -23.196, 0.437, 24.015, 175.589
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                791.1015
## Greenspace_1000m_10pcnt                                                      0.4533
## Age                                                                        -37.1768
## Sex                                                                         23.9573
## BMI                                                                         -5.1525
## EducationCollege or University Degree                                       -1.6088
## EducationCSEs or equivalent                                                  4.8213
## EducationNational Vocational Qualification or equivalent                     2.6814
## EducationNone of the above                                                   4.3628
## EducationO levels/General Certificate of Secondary Education or equivalent   0.8417
## EducationOther professional qualifications                                   4.1920
## Income                                                                      -0.3800
##                                                                            Std. Error
## (Intercept)                                                                    1.4232
## Greenspace_1000m_10pcnt                                                        0.1279
## Age                                                                            0.4772
## Sex                                                                            0.6853
## BMI                                                                            0.3978
## EducationCollege or University Degree                                          1.0143
## EducationCSEs or equivalent                                                    2.1004
## EducationNational Vocational Qualification or equivalent                       1.8006
## EducationNone of the above                                                     2.0102
## EducationO levels/General Certificate of Secondary Education or equivalent     1.1908
## EducationOther professional qualifications                                     1.8494
## Income                                                                         0.3248
##                                                                            t value
## (Intercept)                                                                555.846
## Greenspace_1000m_10pcnt                                                      3.543
## Age                                                                        -77.899
## Sex                                                                         34.956
## BMI                                                                        -12.953
## EducationCollege or University Degree                                       -1.586
## EducationCSEs or equivalent                                                  2.295
## EducationNational Vocational Qualification or equivalent                     1.489
## EducationNone of the above                                                   2.170
## EducationO levels/General Certificate of Secondary Education or equivalent   0.707
## EducationOther professional qualifications                                   2.267
## Income                                                                      -1.170
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    0.000397
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.112744
## EducationCSEs or equivalent                                                0.021729
## EducationNational Vocational Qualification or equivalent                   0.136468
## EducationNone of the above                                                 0.029997
## EducationO levels/General Certificate of Secondary Education or equivalent 0.479676
## EducationOther professional qualifications                                 0.023425
## Income                                                                     0.242082
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.49 on 11436 degrees of freedom
## Multiple R-squared:  0.4519, Adjusted R-squared:  0.4513 
## F-statistic:   857 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                788.3117144
## Greenspace_1000m_10pcnt                                                      0.2025284
## Age                                                                        -38.1122277
## Sex                                                                         22.6138626
## BMI                                                                         -5.9322661
## EducationCollege or University Degree                                       -3.5969815
## EducationCSEs or equivalent                                                  0.7040888
## EducationNational Vocational Qualification or equivalent                    -0.8480647
## EducationNone of the above                                                   0.4225870
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.4924621
## EducationOther professional qualifications                                   0.5669451
## Income                                                                      -1.0167298
##                                                                                 97.5 %
## (Intercept)                                                                793.8913000
## Greenspace_1000m_10pcnt                                                      0.7040734
## Age                                                                        -36.2412821
## Sex                                                                         25.3006609
## BMI                                                                         -4.3727674
## EducationCollege or University Degree                                        0.3794210
## EducationCSEs or equivalent                                                  8.9384154
## EducationNational Vocational Qualification or equivalent                     6.2108699
## EducationNone of the above                                                   8.3030644
## EducationO levels/General Certificate of Secondary Education or equivalent   3.1758938
## EducationOther professional qualifications                                   7.8171422
## Income                                                                       0.2567176

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.019, -22.864, 0.247, 24.055, 178.525
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.563226
## Greenspace_1000m_10pcnt                                                      0.624306
## Age                                                                        -36.934604
## Sex                                                                         23.674363
## BMI                                                                         -4.963924
## EducationCollege or University Degree                                       -1.853993
## EducationCSEs or equivalent                                                  5.171033
## EducationNational Vocational Qualification or equivalent                     3.038026
## EducationNone of the above                                                   5.044845
## EducationO levels/General Certificate of Secondary Education or equivalent   1.021188
## EducationOther professional qualifications                                   4.279764
## Income                                                                      -0.445781
## Average_time_outdoors                                                        0.199942
## Summed_PA_min                                                               -0.004372
## Smoking                                                                     -5.073240
## Disability                                                                  -1.313960
## Deprivation_Index                                                           -0.011630
## Population_density                                                          -1.615714
##                                                                            Std. Error
## (Intercept)                                                                  1.875610
## Greenspace_1000m_10pcnt                                                      0.170492
## Age                                                                          0.479298
## Sex                                                                          0.689665
## BMI                                                                          0.401094
## EducationCollege or University Degree                                        1.012260
## EducationCSEs or equivalent                                                  2.099065
## EducationNational Vocational Qualification or equivalent                     1.796939
## EducationNone of the above                                                   2.014349
## EducationO levels/General Certificate of Secondary Education or equivalent   1.188062
## EducationOther professional qualifications                                   1.843208
## Income                                                                       0.327876
## Average_time_outdoors                                                        0.233954
## Summed_PA_min                                                                0.004030
## Smoking                                                                      0.553593
## Disability                                                                   0.797864
## Deprivation_Index                                                            0.023157
## Population_density                                                           0.726448
##                                                                            t value
## (Intercept)                                                                426.828
## Greenspace_1000m_10pcnt                                                      3.662
## Age                                                                        -77.060
## Sex                                                                         34.327
## BMI                                                                        -12.376
## EducationCollege or University Degree                                       -1.832
## EducationCSEs or equivalent                                                  2.463
## EducationNational Vocational Qualification or equivalent                     1.691
## EducationNone of the above                                                   2.504
## EducationO levels/General Certificate of Secondary Education or equivalent   0.860
## EducationOther professional qualifications                                   2.322
## Income                                                                      -1.360
## Average_time_outdoors                                                        0.855
## Summed_PA_min                                                               -1.085
## Smoking                                                                     -9.164
## Disability                                                                  -1.647
## Deprivation_Index                                                           -0.502
## Population_density                                                          -2.224
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    0.000252
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.067046
## EducationCSEs or equivalent                                                0.013774
## EducationNational Vocational Qualification or equivalent                   0.090928
## EducationNone of the above                                                 0.012278
## EducationO levels/General Certificate of Secondary Education or equivalent 0.390060
## EducationOther professional qualifications                                 0.020255
## Income                                                                     0.173982
## Average_time_outdoors                                                      0.392779
## Summed_PA_min                                                              0.278013
## Smoking                                                                     < 2e-16
## Disability                                                                 0.099617
## Deprivation_Index                                                          0.615517
## Population_density                                                         0.026159
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                   .  
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11430 degrees of freedom
## Multiple R-squared:  0.4563, Adjusted R-squared:  0.4555 
## F-statistic: 564.4 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                796.88670890
## Greenspace_1000m_10pcnt                                                      0.29011160
## Age                                                                        -37.87410963
## Sex                                                                         22.32250172
## BMI                                                                         -5.75013802
## EducationCollege or University Degree                                       -3.83819541
## EducationCSEs or equivalent                                                  1.05650552
## EducationNational Vocational Qualification or equivalent                    -0.48428186
## EducationNone of the above                                                   1.09637560
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.30761698
## EducationOther professional qualifications                                   0.66675934
## Income                                                                      -1.08847361
## Average_time_outdoors                                                       -0.25864820
## Summed_PA_min                                                               -0.01227226
## Smoking                                                                     -6.15837647
## Disability                                                                  -2.87791059
## Deprivation_Index                                                           -0.05702284
## Population_density                                                          -3.03967708
##                                                                                   97.5 %
## (Intercept)                                                                804.239742877
## Greenspace_1000m_10pcnt                                                      0.958500423
## Age                                                                        -35.995097786
## Sex                                                                         25.026225130
## BMI                                                                         -4.177710371
## EducationCollege or University Degree                                        0.130209620
## EducationCSEs or equivalent                                                  9.285561006
## EducationNational Vocational Qualification or equivalent                     6.560334423
## EducationNone of the above                                                   8.993314080
## EducationO levels/General Certificate of Secondary Education or equivalent   3.349992928
## EducationOther professional qualifications                                   7.892769063
## Income                                                                       0.196911596
## Average_time_outdoors                                                        0.658533006
## Summed_PA_min                                                                0.003527808
## Smoking                                                                     -3.988103769
## Disability                                                                   0.249990624
## Deprivation_Index                                                            0.033762209
## Population_density                                                          -0.191751039

Association of greenspace (buffered to 1000m) with white matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.502, -26.165, -1.059, 24.502, 182.085
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                702.4279
## Greenspace_1000m_10pcnt                                                      0.3916
## Age                                                                        -17.3220
## Sex                                                                         -9.3690
## BMI                                                                          0.3295
## EducationCollege or University Degree                                       -2.5623
## EducationCSEs or equivalent                                                  0.9978
## EducationNational Vocational Qualification or equivalent                    -0.2924
## EducationNone of the above                                                   3.6839
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.7411
## EducationOther professional qualifications                                   1.2342
## Income                                                                      -0.2858
##                                                                            Std. Error
## (Intercept)                                                                    1.5438
## Greenspace_1000m_10pcnt                                                        0.1388
## Age                                                                            0.5177
## Sex                                                                            0.7434
## BMI                                                                            0.4315
## EducationCollege or University Degree                                          1.1002
## EducationCSEs or equivalent                                                    2.2784
## EducationNational Vocational Qualification or equivalent                       1.9531
## EducationNone of the above                                                     2.1804
## EducationO levels/General Certificate of Secondary Education or equivalent     1.2917
## EducationOther professional qualifications                                     2.0061
## Income                                                                         0.3523
##                                                                            t value
## (Intercept)                                                                454.995
## Greenspace_1000m_10pcnt                                                      2.822
## Age                                                                        -33.461
## Sex                                                                        -12.603
## BMI                                                                          0.764
## EducationCollege or University Degree                                       -2.329
## EducationCSEs or equivalent                                                  0.438
## EducationNational Vocational Qualification or equivalent                    -0.150
## EducationNone of the above                                                   1.690
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.574
## EducationOther professional qualifications                                   0.615
## Income                                                                      -0.811
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                     0.00479
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.44513
## EducationCollege or University Degree                                       0.01988
## EducationCSEs or equivalent                                                 0.66142
## EducationNational Vocational Qualification or equivalent                    0.88101
## EducationNone of the above                                                  0.09114
## EducationO levels/General Certificate of Secondary Education or equivalent  0.56615
## EducationOther professional qualifications                                  0.53842
## Income                                                                      0.41727
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11436 degrees of freedom
## Multiple R-squared:  0.1012, Adjusted R-squared:  0.1003 
## F-statistic:   117 on 11 and 11436 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                699.4017308
## Greenspace_1000m_10pcnt                                                      0.1195505
## Age                                                                        -18.3366795
## Sex                                                                        -10.8261838
## BMI                                                                         -0.5163213
## EducationCollege or University Degree                                       -4.7188971
## EducationCSEs or equivalent                                                 -3.4681364
## EducationNational Vocational Qualification or equivalent                    -4.1208449
## EducationNone of the above                                                  -0.5901045
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.2730270
## EducationOther professional qualifications                                  -2.6980277
## Income                                                                      -0.9764940
##                                                                                 97.5 %
## (Intercept)                                                                705.4540126
## Greenspace_1000m_10pcnt                                                      0.6635858
## Age                                                                        -16.3072294
## Sex                                                                         -7.9117629
## BMI                                                                          1.1752964
## EducationCollege or University Degree                                       -0.4056182
## EducationCSEs or equivalent                                                  5.4637931
## EducationNational Vocational Qualification or equivalent                     3.5361148
## EducationNone of the above                                                   7.9579982
## EducationO levels/General Certificate of Secondary Education or equivalent   1.7908268
## EducationOther professional qualifications                                   5.1663979
## Income                                                                       0.4048384

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.155, -26.235, -1.27, 24.314, 179.474
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                704.481168
## Greenspace_1000m_10pcnt                                                      0.518381
## Age                                                                        -17.250013
## Sex                                                                         -9.428363
## BMI                                                                          0.434655
## EducationCollege or University Degree                                       -2.540336
## EducationCSEs or equivalent                                                  0.950197
## EducationNational Vocational Qualification or equivalent                    -0.332901
## EducationNone of the above                                                   3.645607
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.752264
## EducationOther professional qualifications                                   1.276914
## Income                                                                      -0.278132
## Average_time_outdoors                                                        0.002700
## Summed_PA_min                                                                0.002865
## Smoking                                                                     -0.639668
## Disability                                                                  -1.111413
## Deprivation_Index                                                           -0.036896
## Population_density                                                          -0.907740
##                                                                            Std. Error
## (Intercept)                                                                  2.042280
## Greenspace_1000m_10pcnt                                                      0.185643
## Age                                                                          0.521889
## Sex                                                                          0.750950
## BMI                                                                          0.436736
## EducationCollege or University Degree                                        1.102211
## EducationCSEs or equivalent                                                  2.285591
## EducationNational Vocational Qualification or equivalent                     1.956618
## EducationNone of the above                                                   2.193347
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293635
## EducationOther professional qualifications                                   2.006999
## Income                                                                       0.357011
## Average_time_outdoors                                                        0.254744
## Summed_PA_min                                                                0.004388
## Smoking                                                                      0.602786
## Disability                                                                   0.868764
## Deprivation_Index                                                            0.025215
## Population_density                                                           0.791002
##                                                                            t value
## (Intercept)                                                                344.948
## Greenspace_1000m_10pcnt                                                      2.792
## Age                                                                        -33.053
## Sex                                                                        -12.555
## BMI                                                                          0.995
## EducationCollege or University Degree                                       -2.305
## EducationCSEs or equivalent                                                  0.416
## EducationNational Vocational Qualification or equivalent                    -0.170
## EducationNone of the above                                                   1.662
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.582
## EducationOther professional qualifications                                   0.636
## Income                                                                      -0.779
## Average_time_outdoors                                                        0.011
## Summed_PA_min                                                                0.653
## Smoking                                                                     -1.061
## Disability                                                                  -1.279
## Deprivation_Index                                                           -1.463
## Population_density                                                          -1.148
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                     0.00524
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.31964
## EducationCollege or University Degree                                       0.02120
## EducationCSEs or equivalent                                                 0.67761
## EducationNational Vocational Qualification or equivalent                    0.86490
## EducationNone of the above                                                  0.09652
## EducationO levels/General Certificate of Secondary Education or equivalent  0.56091
## EducationOther professional qualifications                                  0.52464
## Income                                                                      0.43596
## Average_time_outdoors                                                       0.99154
## Summed_PA_min                                                               0.51384
## Smoking                                                                     0.28863
## Disability                                                                  0.20082
## Deprivation_Index                                                           0.14343
## Population_density                                                          0.25116
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.49 on 11430 degrees of freedom
## Multiple R-squared:  0.1017, Adjusted R-squared:  0.1003 
## F-statistic: 76.11 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                700.477950023
## Greenspace_1000m_10pcnt                                                      0.154489322
## Age                                                                        -18.273005195
## Sex                                                                        -10.900353775
## BMI                                                                         -0.421423234
## EducationCollege or University Degree                                       -4.700857795
## EducationCSEs or equivalent                                                 -3.529954753
## EducationNational Vocational Qualification or equivalent                    -4.168207401
## EducationNone of the above                                                  -0.653729251
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.288010325
## EducationOther professional qualifications                                  -2.657148554
## Income                                                                      -0.977934817
## Average_time_outdoors                                                       -0.496641556
## Summed_PA_min                                                               -0.005736868
## Smoking                                                                     -1.821231098
## Disability                                                                  -2.814339043
## Deprivation_Index                                                           -0.086321956
## Population_density                                                          -2.458238546
##                                                                                  97.5 %
## (Intercept)                                                                708.48438658
## Greenspace_1000m_10pcnt                                                      0.88227226
## Age                                                                        -16.22702130
## Sex                                                                         -7.95637310
## BMI                                                                          1.29073290
## EducationCollege or University Degree                                       -0.37981383
## EducationCSEs or equivalent                                                  5.43034801
## EducationNational Vocational Qualification or equivalent                     3.50240497
## EducationNone of the above                                                   7.94494405
## EducationO levels/General Certificate of Secondary Education or equivalent   1.78348239
## EducationOther professional qualifications                                   5.21097617
## Income                                                                       0.42167182
## Average_time_outdoors                                                        0.50204187
## Summed_PA_min                                                                0.01146722
## Smoking                                                                      0.54189557
## Disability                                                                   0.59151257
## Deprivation_Index                                                            0.01253040
## Population_density                                                           0.64275885

Association of greenspace (buffered to 1000m) with hippocampal volume (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5874, -0.3089, 0.0246, 0.3407, 5.6648
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.915e+00
## Greenspace_1000m_10pcnt                                                     8.563e-05
## Age                                                                        -2.188e-01
## Sex                                                                         2.823e-01
## BMI                                                                        -1.664e-02
## EducationCollege or University Degree                                       2.596e-02
## EducationCSEs or equivalent                                                 5.497e-02
## EducationNational Vocational Qualification or equivalent                    5.704e-02
## EducationNone of the above                                                  5.107e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.588e-02
## EducationOther professional qualifications                                  1.565e-02
## Income                                                                      3.514e-05
##                                                                            Std. Error
## (Intercept)                                                                 2.108e-02
## Greenspace_1000m_10pcnt                                                     1.894e-03
## Age                                                                         7.065e-03
## Sex                                                                         1.015e-02
## BMI                                                                         5.890e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.113e-02
## EducationNational Vocational Qualification or equivalent                    2.666e-02
## EducationNone of the above                                                  2.976e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.763e-02
## EducationOther professional qualifications                                  2.738e-02
## Income                                                                      4.810e-03
##                                                                            t value
## (Intercept)                                                                233.229
## Greenspace_1000m_10pcnt                                                      0.045
## Age                                                                        -30.974
## Sex                                                                         27.820
## BMI                                                                         -2.825
## EducationCollege or University Degree                                        1.729
## EducationCSEs or equivalent                                                  1.766
## EducationNational Vocational Qualification or equivalent                     2.140
## EducationNone of the above                                                   1.716
## EducationO levels/General Certificate of Secondary Education or equivalent   2.035
## EducationOther professional qualifications                                   0.572
## Income                                                                       0.007
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                     0.96394
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.00474
## EducationCollege or University Degree                                       0.08390
## EducationCSEs or equivalent                                                 0.07743
## EducationNational Vocational Qualification or equivalent                    0.03238
## EducationNone of the above                                                  0.08614
## EducationO levels/General Certificate of Secondary Education or equivalent  0.04186
## EducationOther professional qualifications                                  0.56765
## Income                                                                      0.99417
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                       
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ** 
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5253 on 11430 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1636, Adjusted R-squared:  0.1628 
## F-statistic: 203.3 on 11 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                 4.874104099
## Greenspace_1000m_10pcnt                                                    -0.003627062
## Age                                                                        -0.232671550
## Sex                                                                         0.262406189
## BMI                                                                        -0.028181907
## EducationCollege or University Degree                                      -0.003477089
## EducationCSEs or equivalent                                                -0.006046037
## EducationNational Vocational Qualification or equivalent                    0.004791438
## EducationNone of the above                                                 -0.007258136
## EducationO levels/General Certificate of Secondary Education or equivalent  0.001321399
## EducationOther professional qualifications                                 -0.038017210
## Income                                                                     -0.009392575
##                                                                                  97.5 %
## (Intercept)                                                                 4.956727282
## Greenspace_1000m_10pcnt                                                     0.003798328
## Age                                                                        -0.204975555
## Sex                                                                         0.302186869
## BMI                                                                        -0.005092691
## EducationCollege or University Degree                                       0.055401785
## EducationCSEs or equivalent                                                 0.115988081
## EducationNational Vocational Qualification or equivalent                    0.109288289
## EducationNone of the above                                                  0.109399989
## EducationO levels/General Certificate of Secondary Education or equivalent  0.070442711
## EducationOther professional qualifications                                  0.069311348
## Income                                                                      0.009462859

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6158, -0.3104, 0.0246, 0.339, 5.6406
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Greenspace_1000m_10pcnt                                                     1.273e-03
## Age                                                                        -2.166e-01
## Sex                                                                         2.796e-01
## BMI                                                                        -1.366e-02
## EducationCollege or University Degree                                       2.451e-02
## EducationCSEs or equivalent                                                 5.573e-02
## EducationNational Vocational Qualification or equivalent                    5.859e-02
## EducationNone of the above                                                  5.403e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.678e-02
## EducationOther professional qualifications                                  1.605e-02
## Income                                                                     -3.965e-04
## Average_time_outdoors                                                      -8.007e-06
## Summed_PA_min                                                               6.114e-05
## Smoking                                                                    -3.754e-02
## Disability                                                                 -2.217e-02
## Deprivation_Index                                                           6.560e-05
## Population_density                                                         -1.233e-02
##                                                                            Std. Error
## (Intercept)                                                                 2.785e-02
## Greenspace_1000m_10pcnt                                                     2.532e-03
## Age                                                                         7.116e-03
## Sex                                                                         1.024e-02
## BMI                                                                         5.956e-03
## EducationCollege or University Degree                                       1.503e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.991e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.869e-03
## Average_time_outdoors                                                       3.473e-03
## Summed_PA_min                                                               5.984e-05
## Smoking                                                                     8.220e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.439e-04
## Population_density                                                          1.079e-02
##                                                                            t value
## (Intercept)                                                                178.750
## Greenspace_1000m_10pcnt                                                      0.503
## Age                                                                        -30.442
## Sex                                                                         27.300
## BMI                                                                         -2.294
## EducationCollege or University Degree                                        1.631
## EducationCSEs or equivalent                                                  1.786
## EducationNational Vocational Qualification or equivalent                     2.196
## EducationNone of the above                                                   1.807
## EducationO levels/General Certificate of Secondary Education or equivalent   2.085
## EducationOther professional qualifications                                   0.587
## Income                                                                      -0.081
## Average_time_outdoors                                                       -0.002
## Summed_PA_min                                                                1.022
## Smoking                                                                     -4.568
## Disability                                                                  -1.871
## Deprivation_Index                                                            0.191
## Population_density                                                          -1.143
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                      0.6150
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0218
## EducationCollege or University Degree                                        0.1030
## EducationCSEs or equivalent                                                  0.0741
## EducationNational Vocational Qualification or equivalent                     0.0281
## EducationNone of the above                                                   0.0708
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0371
## EducationOther professional qualifications                                   0.5575
## Income                                                                       0.9351
## Average_time_outdoors                                                        0.9982
## Summed_PA_min                                                                0.3069
## Smoking                                                                    4.98e-06
## Disability                                                                   0.0614
## Deprivation_Index                                                            0.8487
## Population_density                                                           0.2530
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                       
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11424 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.1644 
## F-statistic: 133.4 on 17 and 11424 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.924100e+00
## Greenspace_1000m_10pcnt                                                    -3.689250e-03
## Age                                                                        -2.305623e-01
## Sex                                                                         2.594936e-01
## BMI                                                                        -2.533834e-02
## EducationCollege or University Degree                                      -4.954517e-03
## EducationCSEs or equivalent                                                -5.423429e-03
## EducationNational Vocational Qualification or equivalent                    6.292335e-03
## EducationNone of the above                                                 -4.590076e-03
## EducationO levels/General Certificate of Secondary Education or equivalent  2.203203e-03
## EducationOther professional qualifications                                 -3.759028e-02
## Income                                                                     -9.940122e-03
## Average_time_outdoors                                                      -6.816619e-03
## Summed_PA_min                                                              -5.614812e-05
## Smoking                                                                    -5.365679e-02
## Disability                                                                 -4.539523e-02
## Deprivation_Index                                                          -6.084138e-04
## Population_density                                                         -3.347245e-02
##                                                                                   97.5 %
## (Intercept)                                                                 5.0332925131
## Greenspace_1000m_10pcnt                                                     0.0062359466
## Age                                                                        -0.2026662382
## Sex                                                                         0.2996398121
## BMI                                                                        -0.0019900310
## EducationCollege or University Degree                                       0.0539777450
## EducationCSEs or equivalent                                                 0.1168803491
## EducationNational Vocational Qualification or equivalent                    0.1108804975
## EducationNone of the above                                                  0.1126514985
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0713660575
## EducationOther professional qualifications                                  0.0696917738
## Income                                                                      0.0091471803
## Average_time_outdoors                                                       0.0068006043
## Summed_PA_min                                                               0.0001784326
## Smoking                                                                    -0.0214327628
## Disability                                                                  0.0010616439
## Deprivation_Index                                                           0.0007396142
## Population_density                                                          0.0088116145

Moderation by sex: Grey Matter (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -170.961, -22.812, 0.231, 24.041, 178.839
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.569375
## Greenspace_1000m_10pcnt                                                      0.633534
## Sex                                                                         26.378095
## Age                                                                        -36.943359
## BMI                                                                         -4.964385
## EducationCollege or University Degree                                       -1.877046
## EducationCSEs or equivalent                                                  5.125468
## EducationNational Vocational Qualification or equivalent                     2.989042
## EducationNone of the above                                                   5.112315
## EducationO levels/General Certificate of Secondary Education or equivalent   1.031164
## EducationOther professional qualifications                                   4.289145
## Income                                                                      -0.447281
## Average_time_outdoors                                                        0.187739
## Summed_PA_min                                                               -0.004363
## Smoking                                                                     -5.080611
## Disability                                                                  -1.318477
## Deprivation_Index                                                           -0.011743
## Population_density                                                          -1.623409
## Greenspace_1000m_10pcnt:Sex                                                 -0.612674
##                                                                            Std. Error
## (Intercept)                                                                  1.875216
## Greenspace_1000m_10pcnt                                                      0.170499
## Sex                                                                          1.315721
## Age                                                                          0.479210
## BMI                                                                          0.401010
## EducationCollege or University Degree                                        1.012091
## EducationCSEs or equivalent                                                  2.098707
## EducationNational Vocational Qualification or equivalent                     1.796675
## EducationNone of the above                                                   2.014118
## EducationO levels/General Certificate of Secondary Education or equivalent   1.187818
## EducationOther professional qualifications                                   1.842824
## Income                                                                       0.327807
## Average_time_outdoors                                                        0.233960
## Summed_PA_min                                                                0.004029
## Smoking                                                                      0.553484
## Disability                                                                   0.797698
## Deprivation_Index                                                            0.023153
## Population_density                                                           0.726302
## Greenspace_1000m_10pcnt:Sex                                                  0.253926
##                                                                            t value
## (Intercept)                                                                426.921
## Greenspace_1000m_10pcnt                                                      3.716
## Sex                                                                         20.048
## Age                                                                        -77.092
## BMI                                                                        -12.380
## EducationCollege or University Degree                                       -1.855
## EducationCSEs or equivalent                                                  2.442
## EducationNational Vocational Qualification or equivalent                     1.664
## EducationNone of the above                                                   2.538
## EducationO levels/General Certificate of Secondary Education or equivalent   0.868
## EducationOther professional qualifications                                   2.327
## Income                                                                      -1.364
## Average_time_outdoors                                                        0.802
## Summed_PA_min                                                               -1.083
## Smoking                                                                     -9.179
## Disability                                                                  -1.653
## Deprivation_Index                                                           -0.507
## Population_density                                                          -2.235
## Greenspace_1000m_10pcnt:Sex                                                 -2.413
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                    0.000204
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                      0.063676
## EducationCSEs or equivalent                                                0.014613
## EducationNational Vocational Qualification or equivalent                   0.096209
## EducationNone of the above                                                 0.011154
## EducationO levels/General Certificate of Secondary Education or equivalent 0.385349
## EducationOther professional qualifications                                 0.019957
## Income                                                                     0.172449
## Average_time_outdoors                                                      0.422315
## Summed_PA_min                                                              0.278972
## Smoking                                                                     < 2e-16
## Disability                                                                 0.098388
## Deprivation_Index                                                          0.612009
## Population_density                                                         0.025425
## Greenspace_1000m_10pcnt:Sex                                                0.015846
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ***
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                   .  
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         *  
## Greenspace_1000m_10pcnt:Sex                                                *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11429 degrees of freedom
## Multiple R-squared:  0.4566, Adjusted R-squared:  0.4558 
## F-statistic: 533.6 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                796.89362998
## Greenspace_1000m_10pcnt                                                      0.29932552
## Sex                                                                         23.79905502
## Age                                                                        -37.88269389
## BMI                                                                         -5.75043338
## EducationCollege or University Degree                                       -3.86091846
## EducationCSEs or equivalent                                                  1.01164091
## EducationNational Vocational Qualification or equivalent                    -0.53274875
## EducationNone of the above                                                   1.16429742
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.29716372
## EducationOther professional qualifications                                   0.67689394
## Income                                                                      -1.08983889
## Average_time_outdoors                                                       -0.27086255
## Summed_PA_min                                                               -0.01226097
## Smoking                                                                     -6.16553469
## Disability                                                                  -2.88210251
## Deprivation_Index                                                           -0.05712654
## Population_density                                                          -3.04708525
## Greenspace_1000m_10pcnt:Sex                                                 -1.11041241
##                                                                                   97.5 %
## (Intercept)                                                                804.245120402
## Greenspace_1000m_10pcnt                                                      0.967741583
## Sex                                                                         28.957134497
## Age                                                                        -36.004024366
## BMI                                                                         -4.178337090
## EducationCollege or University Degree                                        0.106826653
## EducationCSEs or equivalent                                                  9.239294449
## EducationNational Vocational Qualification or equivalent                     6.510831910
## EducationNone of the above                                                   9.060331907
## EducationO levels/General Certificate of Secondary Education or equivalent   3.359492366
## EducationOther professional qualifications                                   7.901396179
## Income                                                                       0.195277609
## Average_time_outdoors                                                        0.646339638
## Summed_PA_min                                                                0.003535775
## Smoking                                                                     -3.995686532
## Disability                                                                   0.245147821
## Deprivation_Index                                                            0.033639546
## Population_density                                                          -0.199732230
## Greenspace_1000m_10pcnt:Sex                                                 -0.114936463

Moderation by sex: White Matter (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.312, -26.203, -1.204, 24.361, 179.079
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                704.483245
## Greenspace_1000m_10pcnt                                                      0.521497
## Sex                                                                         -8.515382
## Age                                                                        -17.252970
## BMI                                                                          0.434499
## EducationCollege or University Degree                                       -2.548120
## EducationCSEs or equivalent                                                  0.934810
## EducationNational Vocational Qualification or equivalent                    -0.349442
## EducationNone of the above                                                   3.668390
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.748895
## EducationOther professional qualifications                                   1.280081
## Income                                                                      -0.278638
## Average_time_outdoors                                                       -0.001421
## Summed_PA_min                                                                0.002868
## Smoking                                                                     -0.642157
## Disability                                                                  -1.112939
## Deprivation_Index                                                           -0.036934
## Population_density                                                          -0.910338
## Greenspace_1000m_10pcnt:Sex                                                 -0.206885
##                                                                            Std. Error
## (Intercept)                                                                  2.042321
## Greenspace_1000m_10pcnt                                                      0.185693
## Sex                                                                          1.432968
## Age                                                                          0.521914
## BMI                                                                          0.436745
## EducationCollege or University Degree                                        1.102281
## EducationCSEs or equivalent                                                  2.285728
## EducationNational Vocational Qualification or equivalent                     1.956780
## EducationNone of the above                                                   2.193601
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293668
## EducationOther professional qualifications                                   2.007042
## Income                                                                       0.357019
## Average_time_outdoors                                                        0.254808
## Summed_PA_min                                                                0.004388
## Smoking                                                                      0.602806
## Disability                                                                   0.868783
## Deprivation_Index                                                            0.025216
## Population_density                                                           0.791024
## Greenspace_1000m_10pcnt:Sex                                                  0.276554
##                                                                            t value
## (Intercept)                                                                344.943
## Greenspace_1000m_10pcnt                                                      2.808
## Sex                                                                         -5.942
## Age                                                                        -33.057
## BMI                                                                          0.995
## EducationCollege or University Degree                                       -2.312
## EducationCSEs or equivalent                                                  0.409
## EducationNational Vocational Qualification or equivalent                    -0.179
## EducationNone of the above                                                   1.672
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.579
## EducationOther professional qualifications                                   0.638
## Income                                                                      -0.780
## Average_time_outdoors                                                       -0.006
## Summed_PA_min                                                                0.654
## Smoking                                                                     -1.065
## Disability                                                                  -1.281
## Deprivation_Index                                                           -1.465
## Population_density                                                          -1.151
## Greenspace_1000m_10pcnt:Sex                                                 -0.748
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                     0.00499
## Sex                                                                        2.89e-09
## Age                                                                         < 2e-16
## BMI                                                                         0.31983
## EducationCollege or University Degree                                       0.02081
## EducationCSEs or equivalent                                                 0.68256
## EducationNational Vocational Qualification or equivalent                    0.85827
## EducationNone of the above                                                  0.09449
## EducationO levels/General Certificate of Secondary Education or equivalent  0.56267
## EducationOther professional qualifications                                  0.52362
## Income                                                                      0.43514
## Average_time_outdoors                                                       0.99555
## Summed_PA_min                                                               0.51337
## Smoking                                                                     0.28677
## Disability                                                                  0.20021
## Deprivation_Index                                                           0.14303
## Population_density                                                          0.24982
## Greenspace_1000m_10pcnt:Sex                                                 0.45443
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                    ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_1000m_10pcnt:Sex                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11429 degrees of freedom
## Multiple R-squared:  0.1017, Adjusted R-squared:  0.1003 
## F-statistic: 71.91 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                700.479945633
## Greenspace_1000m_10pcnt                                                      0.157506635
## Sex                                                                        -11.324245542
## Age                                                                        -18.276010726
## BMI                                                                         -0.421595512
## EducationCollege or University Degree                                       -4.708780134
## EducationCSEs or equivalent                                                 -3.545608840
## EducationNational Vocational Qualification or equivalent                    -4.185067096
## EducationNone of the above                                                  -0.631443687
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.284705802
## EducationOther professional qualifications                                  -2.654065454
## Income                                                                      -0.978455951
## Average_time_outdoors                                                       -0.500888848
## Summed_PA_min                                                               -0.005733786
## Smoking                                                                     -1.823760696
## Disability                                                                  -2.815901953
## Deprivation_Index                                                           -0.086361230
## Population_density                                                          -2.460881675
## Greenspace_1000m_10pcnt:Sex                                                 -0.748977178
##                                                                                  97.5 %
## (Intercept)                                                                708.48654390
## Greenspace_1000m_10pcnt                                                      0.88548676
## Sex                                                                         -5.70651800
## Age                                                                        -16.22992873
## BMI                                                                          1.29059382
## EducationCollege or University Degree                                       -0.38746033
## EducationCSEs or equivalent                                                  5.41522941
## EducationNational Vocational Qualification or equivalent                     3.48618288
## EducationNone of the above                                                   7.96822419
## EducationO levels/General Certificate of Secondary Education or equivalent   1.78691538
## EducationOther professional qualifications                                   5.21422843
## Income                                                                       0.42118017
## Average_time_outdoors                                                        0.49804729
## Summed_PA_min                                                                0.01147064
## Smoking                                                                      0.53944751
## Disability                                                                   0.59002468
## Deprivation_Index                                                            0.01249323
## Population_density                                                           0.64020538
## Greenspace_1000m_10pcnt:Sex                                                  0.33520787

Moderation by sex: Average hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Greenspace_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Greenspace_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6146, -0.3101, 0.0245, 0.3388, 5.6413
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Greenspace_1000m_10pcnt                                                     1.285e-03
## Sex                                                                         2.830e-01
## Age                                                                        -2.166e-01
## BMI                                                                        -1.366e-02
## EducationCollege or University Degree                                       2.448e-02
## EducationCSEs or equivalent                                                 5.567e-02
## EducationNational Vocational Qualification or equivalent                    5.852e-02
## EducationNone of the above                                                  5.412e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.680e-02
## EducationOther professional qualifications                                  1.606e-02
## Income                                                                     -3.984e-04
## Average_time_outdoors                                                      -2.354e-05
## Summed_PA_min                                                               6.115e-05
## Smoking                                                                    -3.755e-02
## Disability                                                                 -2.217e-02
## Deprivation_Index                                                           6.546e-05
## Population_density                                                         -1.234e-02
## Greenspace_1000m_10pcnt:Sex                                                -7.752e-04
##                                                                            Std. Error
## (Intercept)                                                                 2.785e-02
## Greenspace_1000m_10pcnt                                                     2.532e-03
## Sex                                                                         1.954e-02
## Age                                                                         7.116e-03
## BMI                                                                         5.956e-03
## EducationCollege or University Degree                                       1.503e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.991e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.737e-02
## Income                                                                      4.869e-03
## Average_time_outdoors                                                       3.474e-03
## Summed_PA_min                                                               5.984e-05
## Smoking                                                                     8.220e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.439e-04
## Population_density                                                          1.079e-02
## Greenspace_1000m_10pcnt:Sex                                                 3.771e-03
##                                                                            t value
## (Intercept)                                                                178.743
## Greenspace_1000m_10pcnt                                                      0.507
## Sex                                                                         14.481
## Age                                                                        -30.441
## BMI                                                                         -2.294
## EducationCollege or University Degree                                        1.628
## EducationCSEs or equivalent                                                  1.784
## EducationNational Vocational Qualification or equivalent                     2.193
## EducationNone of the above                                                   1.809
## EducationO levels/General Certificate of Secondary Education or equivalent   2.086
## EducationOther professional qualifications                                   0.587
## Income                                                                      -0.082
## Average_time_outdoors                                                       -0.007
## Summed_PA_min                                                                1.022
## Smoking                                                                     -4.569
## Disability                                                                  -1.871
## Deprivation_Index                                                            0.190
## Population_density                                                          -1.144
## Greenspace_1000m_10pcnt:Sex                                                 -0.206
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_1000m_10pcnt                                                      0.6119
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0218
## EducationCollege or University Degree                                        0.1035
## EducationCSEs or equivalent                                                  0.0744
## EducationNational Vocational Qualification or equivalent                     0.0283
## EducationNone of the above                                                   0.0704
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0370
## EducationOther professional qualifications                                   0.5573
## Income                                                                       0.9348
## Average_time_outdoors                                                        0.9946
## Summed_PA_min                                                                0.3068
## Smoking                                                                    4.96e-06
## Disability                                                                   0.0614
## Deprivation_Index                                                            0.8490
## Population_density                                                           0.2526
## Greenspace_1000m_10pcnt:Sex                                                  0.8371
##                                                                               
## (Intercept)                                                                ***
## Greenspace_1000m_10pcnt                                                       
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_1000m_10pcnt:Sex                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5249 on 11423 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.1643 
## F-statistic:   126 on 18 and 11423 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.924107e+00
## Greenspace_1000m_10pcnt                                                    -3.678994e-03
## Sex                                                                         2.446812e-01
## Age                                                                        -2.305744e-01
## BMI                                                                        -2.533937e-02
## EducationCollege or University Degree                                      -4.986879e-03
## EducationCSEs or equivalent                                                -5.491137e-03
## EducationNational Vocational Qualification or equivalent                    6.224269e-03
## EducationNone of the above                                                 -4.513203e-03
## EducationO levels/General Certificate of Secondary Education or equivalent  2.213838e-03
## EducationOther professional qualifications                                 -3.758146e-02
## Income                                                                     -9.942510e-03
## Average_time_outdoors                                                      -6.834053e-03
## Summed_PA_min                                                              -5.614296e-05
## Smoking                                                                    -5.366746e-02
## Disability                                                                 -4.540174e-02
## Deprivation_Index                                                          -6.085786e-04
## Population_density                                                         -3.348347e-02
## Greenspace_1000m_10pcnt:Sex                                                -8.167627e-03
##                                                                                   97.5 %
## (Intercept)                                                                 5.0333044344
## Greenspace_1000m_10pcnt                                                     0.0062491370
## Sex                                                                         0.3212949696
## Age                                                                        -0.2026763830
## BMI                                                                        -0.0019900838
## EducationCollege or University Degree                                       0.0539505870
## EducationCSEs or equivalent                                                 0.1168235332
## EducationNational Vocational Qualification or equivalent                    0.1108236048
## EducationNone of the above                                                  0.1127444742
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0713799889
## EducationOther professional qualifications                                  0.0697052978
## Income                                                                      0.0091456291
## Average_time_outdoors                                                       0.0067869647
## Summed_PA_min                                                               0.0001784477
## Smoking                                                                    -0.0214415461
## Disability                                                                  0.0010571945
## Deprivation_Index                                                           0.0007395083
## Population_density                                                          0.0088027923
## Greenspace_1000m_10pcnt:Sex                                                 0.0066171947

10.1.2) 300m greenspace buffer

Association of greenspace (buffered to 300m) with grey matter volume (significant)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.197, -22.718, 0.254, 23.921, 179.9
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                801.667833
## Greenspace_300m_10pcnt                                                       0.678362
## Age                                                                        -36.911295
## Sex                                                                         23.630188
## BMI                                                                         -4.952758
## EducationCollege or University Degree                                       -1.955832
## EducationCSEs or equivalent                                                  5.143543
## EducationNational Vocational Qualification or equivalent                     2.936738
## EducationNone of the above                                                   4.976050
## EducationO levels/General Certificate of Secondary Education or equivalent   1.028844
## EducationOther professional qualifications                                   4.302379
## Income                                                                      -0.480944
## Average_time_outdoors                                                        0.184629
## Summed_PA_min                                                               -0.004318
## Smoking                                                                     -5.112520
## Disability                                                                  -1.356159
## Deprivation_Index                                                           -0.010403
## Population_density                                                          -1.694276
##                                                                            Std. Error
## (Intercept)                                                                  1.866954
## Greenspace_300m_10pcnt                                                       0.159504
## Age                                                                          0.478933
## Sex                                                                          0.689335
## BMI                                                                          0.400982
## EducationCollege or University Degree                                        1.011052
## EducationCSEs or equivalent                                                  2.098628
## EducationNational Vocational Qualification or equivalent                     1.796723
## EducationNone of the above                                                   2.013929
## EducationO levels/General Certificate of Secondary Education or equivalent   1.187779
## EducationOther professional qualifications                                   1.842816
## Income                                                                       0.327920
## Average_time_outdoors                                                        0.233998
## Summed_PA_min                                                                0.004029
## Smoking                                                                      0.552797
## Disability                                                                   0.797769
## Deprivation_Index                                                            0.023151
## Population_density                                                           0.695494
##                                                                            t value
## (Intercept)                                                                429.399
## Greenspace_300m_10pcnt                                                       4.253
## Age                                                                        -77.070
## Sex                                                                         34.280
## BMI                                                                        -12.352
## EducationCollege or University Degree                                       -1.934
## EducationCSEs or equivalent                                                  2.451
## EducationNational Vocational Qualification or equivalent                     1.634
## EducationNone of the above                                                   2.471
## EducationO levels/General Certificate of Secondary Education or equivalent   0.866
## EducationOther professional qualifications                                   2.335
## Income                                                                      -1.467
## Average_time_outdoors                                                        0.789
## Summed_PA_min                                                               -1.072
## Smoking                                                                     -9.248
## Disability                                                                  -1.700
## Deprivation_Index                                                           -0.449
## Population_density                                                          -2.436
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                     2.13e-05
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                        0.0531
## EducationCSEs or equivalent                                                  0.0143
## EducationNational Vocational Qualification or equivalent                     0.1022
## EducationNone of the above                                                   0.0135
## EducationO levels/General Certificate of Secondary Education or equivalent   0.3864
## EducationOther professional qualifications                                   0.0196
## Income                                                                       0.1425
## Average_time_outdoors                                                        0.4301
## Summed_PA_min                                                                0.2839
## Smoking                                                                     < 2e-16
## Disability                                                                   0.0892
## Deprivation_Index                                                            0.6532
## Population_density                                                           0.0149
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                     ***
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                *  
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                 *  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.35 on 11430 degrees of freedom
## Multiple R-squared:  0.4566, Adjusted R-squared:  0.4558 
## F-statistic: 564.9 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                798.00828222
## Greenspace_300m_10pcnt                                                       0.36570616
## Age                                                                        -37.85008486
## Sex                                                                         22.27897295
## BMI                                                                         -5.73875243
## EducationCollege or University Degree                                       -3.93766796
## EducationCSEs or equivalent                                                  1.02987203
## EducationNational Vocational Qualification or equivalent                    -0.58514798
## EducationNone of the above                                                   1.02840356
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.29940756
## EducationOther professional qualifications                                   0.69014374
## Income                                                                      -1.12372404
## Average_time_outdoors                                                       -0.27404617
## Summed_PA_min                                                               -0.01221650
## Smoking                                                                     -6.19609706
## Disability                                                                  -2.91992339
## Deprivation_Index                                                           -0.05578323
## Population_density                                                          -3.05756375
##                                                                                   97.5 %
## (Intercept)                                                                805.327383502
## Greenspace_300m_10pcnt                                                       0.991017012
## Age                                                                        -35.972504191
## Sex                                                                         24.981402671
## BMI                                                                         -4.166764262
## EducationCollege or University Degree                                        0.026004385
## EducationCSEs or equivalent                                                  9.257213259
## EducationNational Vocational Qualification or equivalent                     6.458623130
## EducationNone of the above                                                   8.923696360
## EducationO levels/General Certificate of Secondary Education or equivalent   3.357094768
## EducationOther professional qualifications                                   7.914614641
## Income                                                                       0.161835900
## Average_time_outdoors                                                        0.643304760
## Summed_PA_min                                                                0.003579871
## Smoking                                                                     -4.028942114
## Disability                                                                   0.207606239
## Deprivation_Index                                                            0.034976982
## Population_density                                                          -0.330988837

Association of greenspace (buffered to 300m) with white matter volume (significant)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.576, -26.155, -1.211, 24.384, 181.103
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                705.330310
## Greenspace_300m_10pcnt                                                       0.442217
## Age                                                                        -17.221952
## Sex                                                                         -9.468019
## BMI                                                                          0.445383
## EducationCollege or University Degree                                       -2.638313
## EducationCSEs or equivalent                                                  0.928334
## EducationNational Vocational Qualification or equivalent                    -0.399284
## EducationNone of the above                                                   3.594426
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.737902
## EducationOther professional qualifications                                   1.296726
## Income                                                                      -0.300832
## Average_time_outdoors                                                       -0.002971
## Summed_PA_min                                                                0.002924
## Smoking                                                                     -0.687502
## Disability                                                                  -1.138517
## Deprivation_Index                                                           -0.035915
## Population_density                                                          -0.645607
##                                                                            Std. Error
## (Intercept)                                                                  2.033388
## Greenspace_300m_10pcnt                                                       0.173723
## Age                                                                          0.521628
## Sex                                                                          0.750787
## BMI                                                                          0.436729
## EducationCollege or University Degree                                        1.101185
## EducationCSEs or equivalent                                                  2.285714
## EducationNational Vocational Qualification or equivalent                     1.956895
## EducationNone of the above                                                   2.193465
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293666
## EducationOther professional qualifications                                   2.007097
## Income                                                                       0.357153
## Average_time_outdoors                                                        0.254858
## Summed_PA_min                                                                0.004389
## Smoking                                                                      0.602077
## Disability                                                                   0.868888
## Deprivation_Index                                                            0.025215
## Population_density                                                           0.757495
##                                                                            t value
## (Intercept)                                                                346.875
## Greenspace_300m_10pcnt                                                       2.546
## Age                                                                        -33.016
## Sex                                                                        -12.611
## BMI                                                                          1.020
## EducationCollege or University Degree                                       -2.396
## EducationCSEs or equivalent                                                  0.406
## EducationNational Vocational Qualification or equivalent                    -0.204
## EducationNone of the above                                                   1.639
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.570
## EducationOther professional qualifications                                   0.646
## Income                                                                      -0.842
## Average_time_outdoors                                                       -0.012
## Summed_PA_min                                                                0.666
## Smoking                                                                     -1.142
## Disability                                                                  -1.310
## Deprivation_Index                                                           -1.424
## Population_density                                                          -0.852
##                                                                            Pr(>|t|)
## (Intercept)                                                                  <2e-16
## Greenspace_300m_10pcnt                                                       0.0109
## Age                                                                          <2e-16
## Sex                                                                          <2e-16
## BMI                                                                          0.3078
## EducationCollege or University Degree                                        0.0166
## EducationCSEs or equivalent                                                  0.6846
## EducationNational Vocational Qualification or equivalent                     0.8383
## EducationNone of the above                                                   0.1013
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5684
## EducationOther professional qualifications                                   0.5182
## Income                                                                       0.3996
## Average_time_outdoors                                                        0.9907
## Summed_PA_min                                                                0.5053
## Smoking                                                                      0.2535
## Disability                                                                   0.1901
## Deprivation_Index                                                            0.1544
## Population_density                                                           0.3941
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                     *  
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11430 degrees of freedom
## Multiple R-squared:  0.1016, Adjusted R-squared:  0.1002 
## F-statistic: 76.02 on 17 and 11430 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                701.344521252
## Greenspace_300m_10pcnt                                                       0.101689574
## Age                                                                        -18.244433112
## Sex                                                                        -10.939690925
## BMI                                                                         -0.410680459
## EducationCollege or University Degree                                       -4.796824197
## EducationCSEs or equivalent                                                 -3.552057665
## EducationNational Vocational Qualification or equivalent                    -4.235134665
## EducationNone of the above                                                  -0.705140560
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.273709567
## EducationOther professional qualifications                                  -2.637529313
## Income                                                                      -1.000913831
## Average_time_outdoors                                                       -0.502536172
## Summed_PA_min                                                               -0.005678393
## Smoking                                                                     -1.867677104
## Disability                                                                  -2.841687058
## Deprivation_Index                                                           -0.085340446
## Population_density                                                          -2.130427711
##                                                                                  97.5 %
## (Intercept)                                                                709.31609803
## Greenspace_300m_10pcnt                                                       0.78274497
## Age                                                                        -16.19947186
## Sex                                                                         -7.99634786
## BMI                                                                          1.30144564
## EducationCollege or University Degree                                       -0.47980259
## EducationCSEs or equivalent                                                  5.40872587
## EducationNational Vocational Qualification or equivalent                     3.43656710
## EducationNone of the above                                                   7.89399344
## EducationO levels/General Certificate of Secondary Education or equivalent   1.79790570
## EducationOther professional qualifications                                   5.23098107
## Income                                                                       0.39924984
## Average_time_outdoors                                                        0.49659379
## Summed_PA_min                                                                0.01152617
## Smoking                                                                      0.49267308
## Disability                                                                   0.56465227
## Deprivation_Index                                                            0.01351076
## Population_density                                                           0.83921301

Association of greenspace (buffered to 300m) with hippocampal volume (not significant)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6118, -0.3089, 0.0242, 0.3392, 5.6414
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Greenspace_300m_10pcnt                                                     -1.752e-03
## Age                                                                        -2.163e-01
## Sex                                                                         2.794e-01
## BMI                                                                        -1.360e-02
## EducationCollege or University Degree                                       2.395e-02
## EducationCSEs or equivalent                                                 5.571e-02
## EducationNational Vocational Qualification or equivalent                    5.884e-02
## EducationNone of the above                                                  5.404e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.701e-02
## EducationOther professional qualifications                                  1.612e-02
## Income                                                                     -3.006e-04
## Average_time_outdoors                                                       1.433e-04
## Summed_PA_min                                                               6.162e-05
## Smoking                                                                    -3.802e-02
## Disability                                                                 -2.205e-02
## Deprivation_Index                                                           6.712e-05
## Population_density                                                         -4.010e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.773e-02
## Greenspace_300m_10pcnt                                                      2.369e-03
## Age                                                                         7.112e-03
## Sex                                                                         1.024e-02
## BMI                                                                         5.955e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.991e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.736e-02
## Income                                                                      4.870e-03
## Average_time_outdoors                                                       3.475e-03
## Summed_PA_min                                                               5.983e-05
## Smoking                                                                     8.209e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.438e-04
## Population_density                                                          1.033e-02
##                                                                            t value
## (Intercept)                                                                179.567
## Greenspace_300m_10pcnt                                                      -0.740
## Age                                                                        -30.421
## Sex                                                                         27.292
## BMI                                                                         -2.285
## EducationCollege or University Degree                                        1.595
## EducationCSEs or equivalent                                                  1.786
## EducationNational Vocational Qualification or equivalent                     2.205
## EducationNone of the above                                                   1.807
## EducationO levels/General Certificate of Secondary Education or equivalent   2.098
## EducationOther professional qualifications                                   0.589
## Income                                                                      -0.062
## Average_time_outdoors                                                        0.041
## Summed_PA_min                                                                1.030
## Smoking                                                                     -4.631
## Disability                                                                  -1.861
## Deprivation_Index                                                            0.195
## Population_density                                                          -0.388
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                       0.4595
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0224
## EducationCollege or University Degree                                        0.1108
## EducationCSEs or equivalent                                                  0.0741
## EducationNational Vocational Qualification or equivalent                     0.0275
## EducationNone of the above                                                   0.0708
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0360
## EducationOther professional qualifications                                   0.5558
## Income                                                                       0.9508
## Average_time_outdoors                                                        0.9671
## Summed_PA_min                                                                0.3031
## Smoking                                                                    3.68e-06
## Disability                                                                   0.0628
## Deprivation_Index                                                            0.8452
## Population_density                                                           0.6978
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11424 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.1644 
## F-statistic: 133.4 on 17 and 11424 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.9248388288
## Greenspace_300m_10pcnt                                                     -0.0063957853
## Age                                                                        -0.2302815359
## Sex                                                                         0.2593340493
## BMI                                                                        -0.0252780878
## EducationCollege or University Degree                                      -0.0054858806
## EducationCSEs or equivalent                                                -0.0054367141
## EducationNational Vocational Qualification or equivalent                    0.0065374593
## EducationNone of the above                                                 -0.0045797586
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0024257194
## EducationOther professional qualifications                                 -0.0375203936
## Income                                                                     -0.0098473562
## Average_time_outdoors                                                      -0.0066678636
## Summed_PA_min                                                              -0.0000556675
## Smoking                                                                    -0.0541101694
## Disability                                                                 -0.0452839223
## Deprivation_Index                                                          -0.0006068360
## Population_density                                                         -0.0242546540
##                                                                                   97.5 %
## (Intercept)                                                                 5.0335457454
## Greenspace_300m_10pcnt                                                      0.0028910877
## Age                                                                        -0.2024014537
## Sex                                                                         0.2994688984
## BMI                                                                        -0.0019318222
## EducationCollege or University Degree                                       0.0533867007
## EducationCSEs or equivalent                                                 0.1168652045
## EducationNational Vocational Qualification or equivalent                    0.1111329669
## EducationNone of the above                                                  0.1126597091
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0715854342
## EducationOther professional qualifications                                  0.0697594105
## Income                                                                      0.0092461248
## Average_time_outdoors                                                       0.0069544319
## Summed_PA_min                                                               0.0001789033
## Smoking                                                                    -0.0219261820
## Disability                                                                  0.0011760812
## Deprivation_Index                                                           0.0007410800
## Population_density                                                          0.0162346182

Moderation by sex: Grey Matter [Greenspace AND 300m buffer] (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -171.791, -22.68, 0.165, 23.786, 180.346
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                801.820315
## Greenspace_300m_10pcnt                                                       0.560186
## Sex                                                                         25.178883
## Age                                                                        -36.800851
## BMI                                                                         -5.464156
## EducationCollege or University Degree                                       -2.204786
## EducationCSEs or equivalent                                                  4.199983
## EducationNational Vocational Qualification or equivalent                     4.157013
## EducationNone of the above                                                   3.698951
## EducationO levels/General Certificate of Secondary Education or equivalent   1.156039
## EducationOther professional qualifications                                   4.376956
## Income                                                                      -0.490157
## Average_time_outdoors                                                        0.364530
## Summed_PA_min                                                               -0.005944
## Smoking                                                                     -5.090586
## Disability                                                                  -1.736870
## Deprivation_Index                                                           -0.007383
## Population_density                                                          -1.258887
## Greenspace_300m_10pcnt:Sex                                                  -0.739602
##                                                                            Std. Error
## (Intercept)                                                                  2.086813
## Greenspace_300m_10pcnt                                                       0.177769
## Sex                                                                          1.126018
## Age                                                                          0.542788
## BMI                                                                          0.452579
## EducationCollege or University Degree                                        1.124639
## EducationCSEs or equivalent                                                  2.342855
## EducationNational Vocational Qualification or equivalent                     2.030397
## EducationNone of the above                                                   2.218401
## EducationO levels/General Certificate of Secondary Education or equivalent   1.321757
## EducationOther professional qualifications                                   2.062304
## Income                                                                       0.370845
## Average_time_outdoors                                                        0.260152
## Summed_PA_min                                                                0.004461
## Smoking                                                                      0.625057
## Disability                                                                   0.889457
## Deprivation_Index                                                            0.025789
## Population_density                                                           0.777167
## Greenspace_300m_10pcnt:Sex                                                   0.277252
##                                                                            t value
## (Intercept)                                                                384.232
## Greenspace_300m_10pcnt                                                       3.151
## Sex                                                                         22.361
## Age                                                                        -67.800
## BMI                                                                        -12.073
## EducationCollege or University Degree                                       -1.960
## EducationCSEs or equivalent                                                  1.793
## EducationNational Vocational Qualification or equivalent                     2.047
## EducationNone of the above                                                   1.667
## EducationO levels/General Certificate of Secondary Education or equivalent   0.875
## EducationOther professional qualifications                                   2.122
## Income                                                                      -1.322
## Average_time_outdoors                                                        1.401
## Summed_PA_min                                                               -1.332
## Smoking                                                                     -8.144
## Disability                                                                  -1.953
## Deprivation_Index                                                           -0.286
## Population_density                                                          -1.620
## Greenspace_300m_10pcnt:Sex                                                  -2.668
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                      0.00163
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.04997
## EducationCSEs or equivalent                                                 0.07306
## EducationNational Vocational Qualification or equivalent                    0.04065
## EducationNone of the above                                                  0.09547
## EducationO levels/General Certificate of Secondary Education or equivalent  0.38180
## EducationOther professional qualifications                                  0.03383
## Income                                                                      0.18629
## Average_time_outdoors                                                       0.16118
## Summed_PA_min                                                               0.18278
## Smoking                                                                    4.32e-16
## Disability                                                                  0.05088
## Deprivation_Index                                                           0.77468
## Population_density                                                          0.10530
## Greenspace_300m_10pcnt:Sex                                                  0.00765
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                     ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_300m_10pcnt:Sex                                                 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.31 on 9149 degrees of freedom
## Multiple R-squared:  0.4519, Adjusted R-squared:  0.4508 
## F-statistic: 419.1 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                797.72969638
## Greenspace_300m_10pcnt                                                       0.21171909
## Sex                                                                         22.97163655
## Age                                                                        -37.86483630
## BMI                                                                         -6.35131167
## EducationCollege or University Degree                                       -4.40932938
## EducationCSEs or equivalent                                                 -0.39253627
## EducationNational Vocational Qualification or equivalent                     0.17698081
## EducationNone of the above                                                  -0.64961055
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.43489871
## EducationOther professional qualifications                                   0.33437968
## Income                                                                      -1.21709648
## Average_time_outdoors                                                       -0.14542593
## Summed_PA_min                                                               -0.01468938
## Smoking                                                                     -6.31583760
## Disability                                                                  -3.48040363
## Deprivation_Index                                                           -0.05793570
## Population_density                                                          -2.78230688
## Greenspace_300m_10pcnt:Sex                                                  -1.28307841
##                                                                                   97.5 %
## (Intercept)                                                                 8.059109e+02
## Greenspace_300m_10pcnt                                                      9.086528e-01
## Sex                                                                         2.738613e+01
## Age                                                                        -3.573687e+01
## BMI                                                                        -4.577000e+00
## EducationCollege or University Degree                                      -2.434862e-04
## EducationCSEs or equivalent                                                 8.792503e+00
## EducationNational Vocational Qualification or equivalent                    8.137045e+00
## EducationNone of the above                                                  8.047513e+00
## EducationO levels/General Certificate of Secondary Education or equivalent  3.746978e+00
## EducationOther professional qualifications                                  8.419531e+00
## Income                                                                      2.367833e-01
## Average_time_outdoors                                                       8.744850e-01
## Summed_PA_min                                                               2.801124e-03
## Smoking                                                                    -3.865335e+00
## Disability                                                                  6.664295e-03
## Deprivation_Index                                                           4.317049e-02
## Population_density                                                          2.645333e-01
## Greenspace_300m_10pcnt:Sex                                                 -1.961255e-01

Moderation by sex: White Matter [Greenspace AND 300m buffer] (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.347, -26.159, -1.226, 24.364, 181.024
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                705.327879
## Greenspace_300m_10pcnt                                                       0.444438
## Sex                                                                         -8.655423
## Age                                                                        -17.219464
## BMI                                                                          0.442970
## EducationCollege or University Degree                                       -2.643156
## EducationCSEs or equivalent                                                  0.928285
## EducationNational Vocational Qualification or equivalent                    -0.421494
## EducationNone of the above                                                   3.605882
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.733278
## EducationOther professional qualifications                                   1.305782
## Income                                                                      -0.301983
## Average_time_outdoors                                                       -0.008923
## Summed_PA_min                                                                0.002966
## Smoking                                                                     -0.684732
## Disability                                                                  -1.141658
## Deprivation_Index                                                           -0.035903
## Population_density                                                          -0.644721
## Greenspace_300m_10pcnt:Sex                                                  -0.276820
##                                                                            Std. Error
## (Intercept)                                                                  2.033385
## Greenspace_300m_10pcnt                                                       0.173737
## Sex                                                                          1.093382
## Age                                                                          0.521633
## BMI                                                                          0.436734
## EducationCollege or University Degree                                        1.101193
## EducationCSEs or equivalent                                                  2.285710
## EducationNational Vocational Qualification or equivalent                     1.957012
## EducationNone of the above                                                   2.193489
## EducationO levels/General Certificate of Secondary Education or equivalent   1.293672
## EducationOther professional qualifications                                   2.007113
## Income                                                                       0.357154
## Average_time_outdoors                                                        0.254924
## Summed_PA_min                                                                0.004389
## Smoking                                                                      0.602082
## Disability                                                                   0.868892
## Deprivation_Index                                                            0.025215
## Population_density                                                           0.757494
## Greenspace_300m_10pcnt:Sex                                                   0.270779
##                                                                            t value
## (Intercept)                                                                346.874
## Greenspace_300m_10pcnt                                                       2.558
## Sex                                                                         -7.916
## Age                                                                        -33.011
## BMI                                                                          1.014
## EducationCollege or University Degree                                       -2.400
## EducationCSEs or equivalent                                                  0.406
## EducationNational Vocational Qualification or equivalent                    -0.215
## EducationNone of the above                                                   1.644
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.567
## EducationOther professional qualifications                                   0.651
## Income                                                                      -0.846
## Average_time_outdoors                                                       -0.035
## Summed_PA_min                                                                0.676
## Smoking                                                                     -1.137
## Disability                                                                  -1.314
## Deprivation_Index                                                           -1.424
## Population_density                                                          -0.851
## Greenspace_300m_10pcnt:Sex                                                  -1.022
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                       0.0105
## Sex                                                                        2.68e-15
## Age                                                                         < 2e-16
## BMI                                                                          0.3105
## EducationCollege or University Degree                                        0.0164
## EducationCSEs or equivalent                                                  0.6847
## EducationNational Vocational Qualification or equivalent                     0.8295
## EducationNone of the above                                                   0.1002
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5708
## EducationOther professional qualifications                                   0.5153
## Income                                                                       0.3978
## Average_time_outdoors                                                        0.9721
## Summed_PA_min                                                                0.4991
## Smoking                                                                      0.2554
## Disability                                                                   0.1889
## Deprivation_Index                                                            0.1545
## Population_density                                                           0.3947
## Greenspace_300m_10pcnt:Sex                                                   0.3067
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                     *  
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                       
## Disability                                                                    
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_300m_10pcnt:Sex                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.5 on 11429 degrees of freedom
## Multiple R-squared:  0.1017, Adjusted R-squared:  0.1002 
## F-statistic: 71.86 on 18 and 11429 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                701.342095337
## Greenspace_300m_10pcnt                                                       0.103883893
## Sex                                                                        -10.798639585
## Age                                                                        -18.241953982
## BMI                                                                         -0.413103500
## EducationCollege or University Degree                                       -4.801682100
## EducationCSEs or equivalent                                                 -3.552098118
## EducationNational Vocational Qualification or equivalent                    -4.257573833
## EducationNone of the above                                                  -0.693732472
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.269096532
## EducationOther professional qualifications                                  -2.628503570
## Income                                                                      -1.002066891
## Average_time_outdoors                                                       -0.508617233
## Summed_PA_min                                                               -0.005636166
## Smoking                                                                     -1.864917060
## Disability                                                                  -2.844835132
## Deprivation_Index                                                           -0.085328734
## Population_density                                                          -2.129539275
## Greenspace_300m_10pcnt:Sex                                                  -0.807593577
##                                                                                  97.5 %
## (Intercept)                                                                709.31366191
## Greenspace_300m_10pcnt                                                       0.78499117
## Sex                                                                         -6.51220547
## Age                                                                        -16.19697449
## BMI                                                                          1.29904423
## EducationCollege or University Degree                                       -0.48462903
## EducationCSEs or equivalent                                                  5.40866782
## EducationNational Vocational Qualification or equivalent                     3.41458563
## EducationNone of the above                                                   7.90549685
## EducationO levels/General Certificate of Secondary Education or equivalent   1.80253977
## EducationOther professional qualifications                                   5.24006800
## Income                                                                       0.39810099
## Average_time_outdoors                                                        0.49077142
## Summed_PA_min                                                                0.01156914
## Smoking                                                                      0.49545238
## Disability                                                                   0.56151880
## Deprivation_Index                                                            0.01352229
## Population_density                                                           0.84009756
## Greenspace_300m_10pcnt:Sex                                                   0.25395272

Moderation by sex: Average hippocampal volume [Greenspace AND 300m buffer] (not significant) (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Greenspace_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Greenspace_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6149, -0.3083, 0.0232, 0.3389, 5.6369
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.979e+00
## Greenspace_300m_10pcnt                                                     -1.713e-03
## Sex                                                                         2.937e-01
## Age                                                                        -2.163e-01
## BMI                                                                        -1.365e-02
## EducationCollege or University Degree                                       2.386e-02
## EducationCSEs or equivalent                                                 5.569e-02
## EducationNational Vocational Qualification or equivalent                    5.844e-02
## EducationNone of the above                                                  5.424e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  3.709e-02
## EducationOther professional qualifications                                  1.627e-02
## Income                                                                     -3.213e-04
## Average_time_outdoors                                                       3.815e-05
## Summed_PA_min                                                               6.235e-05
## Smoking                                                                    -3.797e-02
## Disability                                                                 -2.211e-02
## Deprivation_Index                                                           6.743e-05
## Population_density                                                         -3.995e-03
## Greenspace_300m_10pcnt:Sex                                                 -4.884e-03
##                                                                            Std. Error
## (Intercept)                                                                 2.773e-02
## Greenspace_300m_10pcnt                                                      2.369e-03
## Sex                                                                         1.491e-02
## Age                                                                         7.111e-03
## BMI                                                                         5.955e-03
## EducationCollege or University Degree                                       1.502e-02
## EducationCSEs or equivalent                                                 3.120e-02
## EducationNational Vocational Qualification or equivalent                    2.668e-02
## EducationNone of the above                                                  2.990e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.764e-02
## EducationOther professional qualifications                                  2.736e-02
## Income                                                                      4.870e-03
## Average_time_outdoors                                                       3.476e-03
## Summed_PA_min                                                               5.983e-05
## Smoking                                                                     8.209e-03
## Disability                                                                  1.185e-02
## Deprivation_Index                                                           3.438e-04
## Population_density                                                          1.033e-02
## Greenspace_300m_10pcnt:Sex                                                  3.692e-03
##                                                                            t value
## (Intercept)                                                                179.571
## Greenspace_300m_10pcnt                                                      -0.723
## Sex                                                                         19.701
## Age                                                                        -30.415
## BMI                                                                         -2.292
## EducationCollege or University Degree                                        1.589
## EducationCSEs or equivalent                                                  1.785
## EducationNational Vocational Qualification or equivalent                     2.190
## EducationNone of the above                                                   1.814
## EducationO levels/General Certificate of Secondary Education or equivalent   2.102
## EducationOther professional qualifications                                   0.595
## Income                                                                      -0.066
## Average_time_outdoors                                                        0.011
## Summed_PA_min                                                                1.042
## Smoking                                                                     -4.625
## Disability                                                                  -1.866
## Deprivation_Index                                                            0.196
## Population_density                                                          -0.387
## Greenspace_300m_10pcnt:Sex                                                  -1.323
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Greenspace_300m_10pcnt                                                       0.4696
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0219
## EducationCollege or University Degree                                        0.1121
## EducationCSEs or equivalent                                                  0.0743
## EducationNational Vocational Qualification or equivalent                     0.0285
## EducationNone of the above                                                   0.0697
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0356
## EducationOther professional qualifications                                   0.5520
## Income                                                                       0.9474
## Average_time_outdoors                                                        0.9912
## Summed_PA_min                                                                0.2974
## Smoking                                                                    3.78e-06
## Disability                                                                   0.0621
## Deprivation_Index                                                            0.8445
## Population_density                                                           0.6989
## Greenspace_300m_10pcnt:Sex                                                   0.1859
##                                                                               
## (Intercept)                                                                ***
## Greenspace_300m_10pcnt                                                        
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                         
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Greenspace_300m_10pcnt:Sex                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5248 on 11423 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1658, Adjusted R-squared:  0.1644 
## F-statistic: 126.1 on 18 and 11423 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.924808e+00
## Greenspace_300m_10pcnt                                                     -6.356657e-03
## Sex                                                                         2.645151e-01
## Age                                                                        -2.302372e-01
## BMI                                                                        -2.531945e-02
## EducationCollege or University Degree                                      -5.573985e-03
## EducationCSEs or equivalent                                                -5.460250e-03
## EducationNational Vocational Qualification or equivalent                    6.140927e-03
## EducationNone of the above                                                 -4.379603e-03
## EducationO levels/General Certificate of Secondary Education or equivalent  2.506995e-03
## EducationOther professional qualifications                                 -3.736374e-02
## Income                                                                     -9.867791e-03
## Average_time_outdoors                                                      -6.774557e-03
## Summed_PA_min                                                              -5.493377e-05
## Smoking                                                                    -5.406359e-02
## Disability                                                                 -4.533772e-02
## Deprivation_Index                                                          -6.065038e-04
## Population_density                                                         -2.423936e-02
## Greenspace_300m_10pcnt:Sex                                                 -1.212104e-02
##                                                                                   97.5 %
## (Intercept)                                                                 5.0335110846
## Greenspace_300m_10pcnt                                                      0.0029306428
## Sex                                                                         0.3229664280
## Age                                                                        -0.2023577047
## BMI                                                                        -0.0019736226
## EducationCollege or University Degree                                       0.0532972528
## EducationCSEs or equivalent                                                 0.1168376789
## EducationNational Vocational Qualification or equivalent                    0.1107395528
## EducationNone of the above                                                  0.1128575010
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0716648505
## EducationOther professional qualifications                                  0.0699135281
## Income                                                                      0.0092251618
## Average_time_outdoors                                                       0.0068508540
## Summed_PA_min                                                               0.0001796394
## Smoking                                                                    -0.0218803723
## Disability                                                                  0.0011210436
## Deprivation_Index                                                           0.0007413683
## Population_density                                                          0.0162486119
## Greenspace_300m_10pcnt:Sex                                                  0.0023530421

10.2) Restrict sample to participants with no change in home location between baseline (2006–2010) and first MRI assessment (2014+)

Required UKB variables: * 699 - Length of time at current address - Instances 2 (measured in units of whole years, except if answer was < 1 year, in which case the value assigned was 0.5 years) * 53 - Date of attending assessment centre - Instances 0 and 2 (format: YYYY-MM-DD) Approach: Include if var 699 (Instance 2) >= Difference in 53 (Instance 2 minus Instance 0) Note: This subset, “NoHomeChange_T2”, was generated in Section 10.3.

10.2.1) 1000m natural environment buffer

Association of natural environment with grey matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -170.797, -23.188, 0.197, 24.033, 175.065
## 
## Coefficients:
##                                                                            Estimate
## (Intercept)                                                                791.3810
## Natural_environment_1000m_10pcnt                                             0.5026
## Age                                                                        -37.0578
## Sex                                                                         23.2780
## BMI                                                                         -5.6691
## EducationCollege or University Degree                                       -1.8663
## EducationCSEs or equivalent                                                  3.9748
## EducationNational Vocational Qualification or equivalent                     3.8337
## EducationNone of the above                                                   3.1045
## EducationO levels/General Certificate of Secondary Education or equivalent   0.9318
## EducationOther professional qualifications                                   4.2213
## Income                                                                      -0.3817
##                                                                            Std. Error
## (Intercept)                                                                    1.6686
## Natural_environment_1000m_10pcnt                                               0.1672
## Age                                                                            0.5404
## Sex                                                                            0.7663
## BMI                                                                            0.4493
## EducationCollege or University Degree                                          1.1283
## EducationCSEs or equivalent                                                    2.3449
## EducationNational Vocational Qualification or equivalent                       2.0339
## EducationNone of the above                                                     2.2113
## EducationO levels/General Certificate of Secondary Education or equivalent     1.3249
## EducationOther professional qualifications                                     2.0700
## Income                                                                         0.3670
##                                                                            t value
## (Intercept)                                                                474.267
## Natural_environment_1000m_10pcnt                                             3.005
## Age                                                                        -68.574
## Sex                                                                         30.378
## BMI                                                                        -12.618
## EducationCollege or University Degree                                       -1.654
## EducationCSEs or equivalent                                                  1.695
## EducationNational Vocational Qualification or equivalent                     1.885
## EducationNone of the above                                                   1.404
## EducationO levels/General Certificate of Secondary Education or equivalent   0.703
## EducationOther professional qualifications                                   2.039
## Income                                                                      -1.040
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00266
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.09814
## EducationCSEs or equivalent                                                 0.09009
## EducationNational Vocational Qualification or equivalent                    0.05948
## EducationNone of the above                                                  0.16039
## EducationO levels/General Certificate of Secondary Education or equivalent  0.48188
## EducationOther professional qualifications                                  0.04145
## Income                                                                      0.29842
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   .  
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.46 on 9156 degrees of freedom
## Multiple R-squared:  0.4469, Adjusted R-squared:  0.4462 
## F-statistic: 672.6 on 11 and 9156 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                788.1101196
## Natural_environment_1000m_10pcnt                                             0.1747642
## Age                                                                        -38.1170706
## Sex                                                                         21.7759741
## BMI                                                                         -6.5498041
## EducationCollege or University Degree                                       -4.0779502
## EducationCSEs or equivalent                                                 -0.6216530
## EducationNational Vocational Qualification or equivalent                    -0.1532227
## EducationNone of the above                                                  -1.2302661
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.6652313
## EducationOther professional qualifications                                   0.1636707
## Income                                                                      -1.1011661
##                                                                                 97.5 %
## (Intercept)                                                                794.6519362
## Natural_environment_1000m_10pcnt                                             0.8303460
## Age                                                                        -35.9984549
## Sex                                                                         24.7800901
## BMI                                                                         -4.7883489
## EducationCollege or University Degree                                        0.3454000
## EducationCSEs or equivalent                                                  8.5712462
## EducationNational Vocational Qualification or equivalent                     7.8207212
## EducationNone of the above                                                   7.4391832
## EducationO levels/General Certificate of Secondary Education or equivalent   3.5287781
## EducationOther professional qualifications                                   8.2789876
## Income                                                                       0.3377997

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -173.009, -22.759, -0.008, 23.958, 178.198
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.175618
## Natural_environment_1000m_10pcnt                                             0.681389
## Age                                                                        -36.814975
## Sex                                                                         23.041793
## BMI                                                                         -5.483452
## EducationCollege or University Degree                                       -2.110404
## EducationCSEs or equivalent                                                  4.156601
## EducationNational Vocational Qualification or equivalent                     4.182685
## EducationNone of the above                                                   3.683638
## EducationO levels/General Certificate of Secondary Education or equivalent   1.085098
## EducationOther professional qualifications                                   4.313293
## Income                                                                      -0.439569
## Average_time_outdoors                                                        0.401500
## Summed_PA_min                                                               -0.006357
## Smoking                                                                     -5.073919
## Disability                                                                  -1.667395
## Deprivation_Index                                                           -0.007759
## Population_density                                                          -1.403465
##                                                                            Std. Error
## (Intercept)                                                                  2.134353
## Natural_environment_1000m_10pcnt                                             0.225570
## Age                                                                          0.542994
## Sex                                                                          0.771623
## BMI                                                                          0.452837
## EducationCollege or University Degree                                        1.125987
## EducationCSEs or equivalent                                                  2.343839
## EducationNational Vocational Qualification or equivalent                     2.031204
## EducationNone of the above                                                   2.219232
## EducationO levels/General Certificate of Secondary Education or equivalent   1.322484
## EducationOther professional qualifications                                   2.063195
## Income                                                                       0.371047
## Average_time_outdoors                                                        0.260034
## Summed_PA_min                                                                0.004463
## Smoking                                                                      0.625589
## Disability                                                                   0.889767
## Deprivation_Index                                                            0.025799
## Population_density                                                           0.822274
##                                                                            t value
## (Intercept)                                                                374.903
## Natural_environment_1000m_10pcnt                                             3.021
## Age                                                                        -67.800
## Sex                                                                         29.861
## BMI                                                                        -12.109
## EducationCollege or University Degree                                       -1.874
## EducationCSEs or equivalent                                                  1.773
## EducationNational Vocational Qualification or equivalent                     2.059
## EducationNone of the above                                                   1.660
## EducationO levels/General Certificate of Secondary Education or equivalent   0.820
## EducationOther professional qualifications                                   2.091
## Income                                                                      -1.185
## Average_time_outdoors                                                        1.544
## Summed_PA_min                                                               -1.424
## Smoking                                                                     -8.111
## Disability                                                                  -1.874
## Deprivation_Index                                                           -0.301
## Population_density                                                          -1.707
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00253
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.06093
## EducationCSEs or equivalent                                                 0.07619
## EducationNational Vocational Qualification or equivalent                    0.03950
## EducationNone of the above                                                  0.09697
## EducationO levels/General Certificate of Secondary Education or equivalent  0.41195
## EducationOther professional qualifications                                  0.03659
## Income                                                                      0.23618
## Average_time_outdoors                                                       0.12262
## Summed_PA_min                                                               0.15442
## Smoking                                                                    5.69e-16
## Disability                                                                  0.06097
## Deprivation_Index                                                           0.76362
## Population_density                                                          0.08789
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.33 on 9150 degrees of freedom
## Multiple R-squared:  0.4514, Adjusted R-squared:  0.4504 
## F-statistic: 442.9 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                795.99180944
## Natural_environment_1000m_10pcnt                                             0.23922184
## Age                                                                        -37.87936380
## Sex                                                                         21.52923990
## BMI                                                                         -6.37111397
## EducationCollege or University Degree                                       -4.31759023
## EducationCSEs or equivalent                                                 -0.43784809
## EducationNational Vocational Qualification or equivalent                     0.20107194
## EducationNone of the above                                                  -0.66655268
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.50726696
## EducationOther professional qualifications                                   0.26896906
## Income                                                                      -1.16690370
## Average_time_outdoors                                                       -0.10822462
## Summed_PA_min                                                               -0.01510585
## Smoking                                                                     -6.30021347
## Disability                                                                  -3.41153760
## Deprivation_Index                                                           -0.05833107
## Population_density                                                          -3.01530660
##                                                                                  97.5 %
## (Intercept)                                                                804.35942681
## Natural_environment_1000m_10pcnt                                             1.12355607
## Age                                                                        -35.75058600
## Sex                                                                         24.55434584
## BMI                                                                         -4.59578947
## EducationCollege or University Degree                                        0.09678217
## EducationCSEs or equivalent                                                  8.75104934
## EducationNational Vocational Qualification or equivalent                     8.16429894
## EducationNone of the above                                                   8.03382861
## EducationO levels/General Certificate of Secondary Education or equivalent   3.67746218
## EducationOther professional qualifications                                   8.35761652
## Income                                                                       0.28776559
## Average_time_outdoors                                                        0.91122491
## Summed_PA_min                                                                0.00239242
## Smoking                                                                     -3.84762392
## Disability                                                                   0.07674677
## Deprivation_Index                                                            0.04281328
## Population_density                                                           0.20837641

Association of natural environment with white matter volume (significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -147.416, -26.126, -1.147, 24.785, 182.458
## 
## Coefficients:
##                                                                             Estimate
## (Intercept)                                                                702.64263
## Natural_environment_1000m_10pcnt                                             0.57288
## Age                                                                        -17.21858
## Sex                                                                         -9.81829
## BMI                                                                          0.04337
## EducationCollege or University Degree                                       -2.80216
## EducationCSEs or equivalent                                                  1.46328
## EducationNational Vocational Qualification or equivalent                     0.33400
## EducationNone of the above                                                   2.28736
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.80409
## EducationOther professional qualifications                                   1.20998
## Income                                                                      -0.53678
##                                                                            Std. Error
## (Intercept)                                                                   1.82489
## Natural_environment_1000m_10pcnt                                              0.18288
## Age                                                                           0.59101
## Sex                                                                           0.83802
## BMI                                                                           0.49137
## EducationCollege or University Degree                                         1.23393
## EducationCSEs or equivalent                                                   2.56443
## EducationNational Vocational Qualification or equivalent                      2.22440
## EducationNone of the above                                                    2.41841
## EducationO levels/General Certificate of Secondary Education or equivalent    1.44891
## EducationOther professional qualifications                                    2.26383
## Income                                                                        0.40141
##                                                                            t value
## (Intercept)                                                                385.032
## Natural_environment_1000m_10pcnt                                             3.133
## Age                                                                        -29.134
## Sex                                                                        -11.716
## BMI                                                                          0.088
## EducationCollege or University Degree                                       -2.271
## EducationCSEs or equivalent                                                  0.571
## EducationNational Vocational Qualification or equivalent                     0.150
## EducationNone of the above                                                   0.946
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.555
## EducationOther professional qualifications                                   0.534
## Income                                                                      -1.337
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00174
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.92967
## EducationCollege or University Degree                                       0.02317
## EducationCSEs or equivalent                                                 0.56828
## EducationNational Vocational Qualification or equivalent                    0.88065
## EducationNone of the above                                                  0.34427
## EducationO levels/General Certificate of Secondary Education or equivalent  0.57893
## EducationOther professional qualifications                                  0.59302
## Income                                                                      0.18118
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.78 on 9156 degrees of freedom
## Multiple R-squared:  0.09787,    Adjusted R-squared:  0.09678 
## F-statistic:  90.3 on 11 and 9156 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                  2.5 %
## (Intercept)                                                                699.0654273
## Natural_environment_1000m_10pcnt                                             0.2143949
## Age                                                                        -18.3770838
## Sex                                                                        -11.4610021
## BMI                                                                         -0.9198304
## EducationCollege or University Degree                                       -5.2209405
## EducationCSEs or equivalent                                                 -3.5635871
## EducationNational Vocational Qualification or equivalent                    -4.0263184
## EducationNone of the above                                                  -2.4532731
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.6442817
## EducationOther professional qualifications                                  -3.2276366
## Income                                                                      -1.3236311
##                                                                                 97.5 %
## (Intercept)                                                                706.2198236
## Natural_environment_1000m_10pcnt                                             0.9313658
## Age                                                                        -16.0600796
## Sex                                                                         -8.1755788
## BMI                                                                          1.0065685
## EducationCollege or University Degree                                       -0.3833851
## EducationCSEs or equivalent                                                  6.4901408
## EducationNational Vocational Qualification or equivalent                     4.6943105
## EducationNone of the above                                                   7.0279887
## EducationO levels/General Certificate of Secondary Education or equivalent   2.0360980
## EducationOther professional qualifications                                   5.6476035
## Income                                                                       0.2500803

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -149.451, -26.141, -1.379, 24.633, 179.262
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                705.605877
## Natural_environment_1000m_10pcnt                                             0.699575
## Age                                                                        -17.112800
## Sex                                                                         -9.899572
## BMI                                                                          0.170480
## EducationCollege or University Degree                                       -2.819271
## EducationCSEs or equivalent                                                  1.378415
## EducationNational Vocational Qualification or equivalent                     0.322354
## EducationNone of the above                                                   2.290773
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.815181
## EducationOther professional qualifications                                   1.226198
## Income                                                                      -0.527892
## Average_time_outdoors                                                        0.082078
## Summed_PA_min                                                                0.001801
## Smoking                                                                     -1.241654
## Disability                                                                  -1.285782
## Deprivation_Index                                                           -0.047664
## Population_density                                                          -0.834810
##                                                                            Std. Error
## (Intercept)                                                                  2.342654
## Natural_environment_1000m_10pcnt                                             0.247584
## Age                                                                          0.595987
## Sex                                                                          0.846929
## BMI                                                                          0.497032
## EducationCollege or University Degree                                        1.235877
## EducationCSEs or equivalent                                                  2.572585
## EducationNational Vocational Qualification or equivalent                     2.229438
## EducationNone of the above                                                   2.435817
## EducationO levels/General Certificate of Secondary Education or equivalent   1.451552
## EducationOther professional qualifications                                   2.264552
## Income                                                                       0.407259
## Average_time_outdoors                                                        0.285412
## Summed_PA_min                                                                0.004899
## Smoking                                                                      0.686643
## Disability                                                                   0.976603
## Deprivation_Index                                                            0.028317
## Population_density                                                           0.902524
##                                                                            t value
## (Intercept)                                                                301.199
## Natural_environment_1000m_10pcnt                                             2.826
## Age                                                                        -28.713
## Sex                                                                        -11.689
## BMI                                                                          0.343
## EducationCollege or University Degree                                       -2.281
## EducationCSEs or equivalent                                                  0.536
## EducationNational Vocational Qualification or equivalent                     0.145
## EducationNone of the above                                                   0.940
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.562
## EducationOther professional qualifications                                   0.541
## Income                                                                      -1.296
## Average_time_outdoors                                                        0.288
## Summed_PA_min                                                                0.368
## Smoking                                                                     -1.808
## Disability                                                                  -1.317
## Deprivation_Index                                                           -1.683
## Population_density                                                          -0.925
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                            0.00473
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         0.73161
## EducationCollege or University Degree                                       0.02256
## EducationCSEs or equivalent                                                 0.59210
## EducationNational Vocational Qualification or equivalent                    0.88504
## EducationNone of the above                                                  0.34701
## EducationO levels/General Certificate of Secondary Education or equivalent  0.57441
## EducationOther professional qualifications                                  0.58819
## Income                                                                      0.19494
## Average_time_outdoors                                                       0.77368
## Summed_PA_min                                                               0.71321
## Smoking                                                                     0.07059
## Disability                                                                  0.18801
## Deprivation_Index                                                           0.09237
## Population_density                                                          0.35500
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    .  
## Disability                                                                    
## Deprivation_Index                                                          .  
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.77 on 9150 degrees of freedom
## Multiple R-squared:  0.09876,    Adjusted R-squared:  0.09709 
## F-statistic: 58.98 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                701.013751493
## Natural_environment_1000m_10pcnt                                             0.214254321
## Age                                                                        -18.281067140
## Sex                                                                        -11.559742095
## BMI                                                                         -0.803813317
## EducationCollege or University Degree                                       -5.241866682
## EducationCSEs or equivalent                                                 -3.664426432
## EducationNational Vocational Qualification or equivalent                    -4.047843098
## EducationNone of the above                                                  -2.483972321
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.660546408
## EducationOther professional qualifications                                  -3.212829800
## Income                                                                      -1.326210117
## Average_time_outdoors                                                       -0.477392848
## Summed_PA_min                                                               -0.007802349
## Smoking                                                                     -2.587628044
## Disability                                                                  -3.200142992
## Deprivation_Index                                                           -0.103171406
## Population_density                                                          -2.603958634
##                                                                                   97.5 %
## (Intercept)                                                                710.198002345
## Natural_environment_1000m_10pcnt                                             1.184894713
## Age                                                                        -15.944532315
## Sex                                                                         -8.239402429
## BMI                                                                          1.144773094
## EducationCollege or University Degree                                       -0.396675786
## EducationCSEs or equivalent                                                  6.421256900
## EducationNational Vocational Qualification or equivalent                     4.692551101
## EducationNone of the above                                                   7.065518382
## EducationO levels/General Certificate of Secondary Education or equivalent   2.030183810
## EducationOther professional qualifications                                   5.665225207
## Income                                                                       0.270426904
## Average_time_outdoors                                                        0.641549357
## Summed_PA_min                                                                0.011403651
## Smoking                                                                      0.104320767
## Disability                                                                   0.628578776
## Deprivation_Index                                                            0.007844074
## Population_density                                                           0.934338128

Association of natural environment with hippocampal volume (not significant)

Crude model (Covariates: Age, Sex, BMI, Education, and Income)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5792, -0.3122, 0.0211, 0.3418, 5.6649
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.9155698
## Natural_environment_1000m_10pcnt                                           -0.0007196
## Age                                                                        -0.2183291
## Sex                                                                         0.2871576
## BMI                                                                        -0.0160913
## EducationCollege or University Degree                                       0.0407363
## EducationCSEs or equivalent                                                 0.0585779
## EducationNational Vocational Qualification or equivalent                    0.0594327
## EducationNone of the above                                                  0.0545458
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0428222
## EducationOther professional qualifications                                  0.0289944
## Income                                                                     -0.0008287
##                                                                            Std. Error
## (Intercept)                                                                 0.0248399
## Natural_environment_1000m_10pcnt                                            0.0024886
## Age                                                                         0.0080416
## Sex                                                                         0.0114054
## BMI                                                                         0.0066873
## EducationCollege or University Degree                                       0.0167951
## EducationCSEs or equivalent                                                 0.0349437
## EducationNational Vocational Qualification or equivalent                    0.0302674
## EducationNone of the above                                                  0.0329073
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0197201
## EducationOther professional qualifications                                  0.0308042
## Income                                                                      0.0054635
##                                                                            t value
## (Intercept)                                                                197.890
## Natural_environment_1000m_10pcnt                                            -0.289
## Age                                                                        -27.150
## Sex                                                                         25.177
## BMI                                                                         -2.406
## EducationCollege or University Degree                                        2.425
## EducationCSEs or equivalent                                                  1.676
## EducationNational Vocational Qualification or equivalent                     1.964
## EducationNone of the above                                                   1.658
## EducationO levels/General Certificate of Secondary Education or equivalent   2.172
## EducationOther professional qualifications                                   0.941
## Income                                                                      -0.152
##                                                                            Pr(>|t|)
## (Intercept)                                                                  <2e-16
## Natural_environment_1000m_10pcnt                                             0.7725
## Age                                                                          <2e-16
## Sex                                                                          <2e-16
## BMI                                                                          0.0161
## EducationCollege or University Degree                                        0.0153
## EducationCSEs or equivalent                                                  0.0937
## EducationNational Vocational Qualification or equivalent                     0.0496
## EducationNone of the above                                                   0.0974
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0299
## EducationOther professional qualifications                                   0.3466
## Income                                                                       0.8794
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5276 on 9150 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1631, Adjusted R-squared:  0.1621 
## F-statistic: 162.1 on 11 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.8668780867
## Natural_environment_1000m_10pcnt                                           -0.0055978818
## Age                                                                        -0.2340924166
## Sex                                                                         0.2648004625
## BMI                                                                        -0.0291998914
## EducationCollege or University Degree                                       0.0078141064
## EducationCSEs or equivalent                                                -0.0099194378
## EducationNational Vocational Qualification or equivalent                    0.0001019073
## EducationNone of the above                                                 -0.0099599657
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0041664672
## EducationOther professional qualifications                                 -0.0313887095
## Income                                                                     -0.0115382819
##                                                                                  97.5 %
## (Intercept)                                                                 4.964261552
## Natural_environment_1000m_10pcnt                                            0.004158592
## Age                                                                        -0.202565856
## Sex                                                                         0.309514710
## BMI                                                                        -0.002982743
## EducationCollege or University Degree                                       0.073658442
## EducationCSEs or equivalent                                                 0.127075311
## EducationNational Vocational Qualification or equivalent                    0.118763444
## EducationNone of the above                                                  0.119051473
## EducationO levels/General Certificate of Secondary Education or equivalent  0.081477923
## EducationOther professional qualifications                                  0.089377466
## Income                                                                      0.009880981

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6085, -0.312, 0.0211, 0.3396, 5.6316
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.984e+00
## Natural_environment_1000m_10pcnt                                            2.002e-03
## Age                                                                        -2.159e-01
## Sex                                                                         2.849e-01
## BMI                                                                        -1.352e-02
## EducationCollege or University Degree                                       3.952e-02
## EducationCSEs or equivalent                                                 5.877e-02
## EducationNational Vocational Qualification or equivalent                    6.123e-02
## EducationNone of the above                                                  5.775e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  4.377e-02
## EducationOther professional qualifications                                  2.971e-02
## Income                                                                     -1.470e-03
## Average_time_outdoors                                                       2.532e-03
## Summed_PA_min                                                              -1.805e-05
## Smoking                                                                    -3.815e-02
## Disability                                                                 -3.061e-02
## Deprivation_Index                                                           1.611e-04
## Population_density                                                         -1.873e-02
##                                                                            Std. Error
## (Intercept)                                                                 3.186e-02
## Natural_environment_1000m_10pcnt                                            3.367e-03
## Age                                                                         8.102e-03
## Sex                                                                         1.152e-02
## BMI                                                                         6.758e-03
## EducationCollege or University Degree                                       1.681e-02
## EducationCSEs or equivalent                                                 3.502e-02
## EducationNational Vocational Qualification or equivalent                    3.031e-02
## EducationNone of the above                                                  3.311e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.974e-02
## EducationOther professional qualifications                                  3.079e-02
## Income                                                                      5.538e-03
## Average_time_outdoors                                                       3.880e-03
## Summed_PA_min                                                               6.660e-05
## Smoking                                                                     9.336e-03
## Disability                                                                  1.328e-02
## Deprivation_Index                                                           3.850e-04
## Population_density                                                          1.227e-02
##                                                                            t value
## (Intercept)                                                                156.436
## Natural_environment_1000m_10pcnt                                             0.595
## Age                                                                        -26.650
## Sex                                                                         24.737
## BMI                                                                         -2.000
## EducationCollege or University Degree                                        2.351
## EducationCSEs or equivalent                                                  1.678
## EducationNational Vocational Qualification or equivalent                     2.020
## EducationNone of the above                                                   1.744
## EducationO levels/General Certificate of Secondary Education or equivalent   2.218
## EducationOther professional qualifications                                   0.965
## Income                                                                      -0.266
## Average_time_outdoors                                                        0.652
## Summed_PA_min                                                               -0.271
## Smoking                                                                     -4.087
## Disability                                                                  -2.305
## Deprivation_Index                                                            0.418
## Population_density                                                          -1.527
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.5521
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0455
## EducationCollege or University Degree                                        0.0187
## EducationCSEs or equivalent                                                  0.0934
## EducationNational Vocational Qualification or equivalent                     0.0434
## EducationNone of the above                                                   0.0812
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0266
## EducationOther professional qualifications                                   0.3346
## Income                                                                       0.7906
## Average_time_outdoors                                                        0.5141
## Summed_PA_min                                                                0.7864
## Smoking                                                                    4.41e-05
## Disability                                                                   0.0212
## Deprivation_Index                                                            0.6757
## Population_density                                                           0.1269
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5271 on 9144 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1654, Adjusted R-squared:  0.1638 
## F-statistic: 106.6 on 17 and 9144 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.9212018769
## Natural_environment_1000m_10pcnt                                           -0.0045972459
## Age                                                                        -0.2318058149
## Sex                                                                         0.2622964049
## BMI                                                                        -0.0267657474
## EducationCollege or University Degree                                       0.0065717897
## EducationCSEs or equivalent                                                -0.0098838093
## EducationNational Vocational Qualification or equivalent                    0.0018126977
## EducationNone of the above                                                 -0.0071622577
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0050791546
## EducationOther professional qualifications                                 -0.0306405100
## Income                                                                     -0.0123262691
## Average_time_outdoors                                                      -0.0050744791
## Summed_PA_min                                                              -0.0001486072
## Smoking                                                                    -0.0564554045
## Disability                                                                 -0.0566517689
## Deprivation_Index                                                          -0.0005936580
## Population_density                                                         -0.0427855890
##                                                                                   97.5 %
## (Intercept)                                                                 5.0460971120
## Natural_environment_1000m_10pcnt                                            0.0086009403
## Age                                                                        -0.2000419378
## Sex                                                                         0.3074435579
## BMI                                                                        -0.0002701720
## EducationCollege or University Degree                                       0.0724627796
## EducationCSEs or equivalent                                                 0.1274147948
## EducationNational Vocational Qualification or equivalent                    0.1206378213
## EducationNone of the above                                                  0.1226621760
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0824629934
## EducationOther professional qualifications                                  0.0900573752
## Income                                                                      0.0093853887
## Average_time_outdoors                                                       0.0101378246
## Summed_PA_min                                                               0.0001125044
## Smoking                                                                    -0.0198542688
## Disability                                                                 -0.0045747303
## Deprivation_Index                                                           0.0009158461
## Population_density                                                          0.0053209322

Moderation by sex: Grey Matter (*not significant, p = 0.054)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.224, -22.898, 0.192, 23.943, 178.515
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                800.176883
## Natural_environment_1000m_10pcnt                                             0.687840
## Sex                                                                         26.097220
## Age                                                                        -36.823583
## BMI                                                                         -5.478067
## EducationCollege or University Degree                                       -2.112426
## EducationCSEs or equivalent                                                  4.117743
## EducationNational Vocational Qualification or equivalent                     4.155908
## EducationNone of the above                                                   3.745138
## EducationO levels/General Certificate of Secondary Education or equivalent   1.115626
## EducationOther professional qualifications                                   4.321789
## Income                                                                      -0.445529
## Average_time_outdoors                                                        0.392056
## Summed_PA_min                                                               -0.006341
## Smoking                                                                     -5.079608
## Disability                                                                  -1.674802
## Deprivation_Index                                                           -0.007766
## Population_density                                                          -1.412503
## Natural_environment_1000m_10pcnt:Sex                                        -0.640973
##                                                                            Std. Error
## (Intercept)                                                                  2.134036
## Natural_environment_1000m_10pcnt                                             0.225561
## Sex                                                                          1.762185
## Age                                                                          0.542931
## BMI                                                                          0.452779
## EducationCollege or University Degree                                        1.125820
## EducationCSEs or equivalent                                                  2.343578
## EducationNational Vocational Qualification or equivalent                     2.030950
## EducationNone of the above                                                   2.219132
## EducationO levels/General Certificate of Secondary Education or equivalent   1.322383
## EducationOther professional qualifications                                   2.062894
## Income                                                                       0.371005
## Average_time_outdoors                                                        0.260042
## Summed_PA_min                                                                0.004463
## Smoking                                                                      0.625503
## Disability                                                                   0.889643
## Deprivation_Index                                                            0.025795
## Population_density                                                           0.822166
## Natural_environment_1000m_10pcnt:Sex                                         0.332362
##                                                                            t value
## (Intercept)                                                                374.959
## Natural_environment_1000m_10pcnt                                             3.049
## Sex                                                                         14.810
## Age                                                                        -67.824
## BMI                                                                        -12.099
## EducationCollege or University Degree                                       -1.876
## EducationCSEs or equivalent                                                  1.757
## EducationNational Vocational Qualification or equivalent                     2.046
## EducationNone of the above                                                   1.688
## EducationO levels/General Certificate of Secondary Education or equivalent   0.844
## EducationOther professional qualifications                                   2.095
## Income                                                                      -1.201
## Average_time_outdoors                                                        1.508
## Summed_PA_min                                                               -1.421
## Smoking                                                                     -8.121
## Disability                                                                  -1.883
## Deprivation_Index                                                           -0.301
## Population_density                                                          -1.718
## Natural_environment_1000m_10pcnt:Sex                                        -1.929
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.0023
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                        0.0606
## EducationCSEs or equivalent                                                  0.0789
## EducationNational Vocational Qualification or equivalent                     0.0408
## EducationNone of the above                                                   0.0915
## EducationO levels/General Certificate of Secondary Education or equivalent   0.3989
## EducationOther professional qualifications                                   0.0362
## Income                                                                       0.2298
## Average_time_outdoors                                                        0.1317
## Summed_PA_min                                                                0.1554
## Smoking                                                                    5.23e-16
## Disability                                                                   0.0598
## Deprivation_Index                                                            0.7634
## Population_density                                                           0.0858
## Natural_environment_1000m_10pcnt:Sex                                         0.0538
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                         .  
## Natural_environment_1000m_10pcnt:Sex                                       .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.32 on 9149 degrees of freedom
## Multiple R-squared:  0.4517, Adjusted R-squared:  0.4506 
## F-statistic: 418.7 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                795.99369532
## Natural_environment_1000m_10pcnt                                             0.24568976
## Sex                                                                         22.64294361
## Age                                                                        -37.88785026
## BMI                                                                         -6.36561382
## EducationCollege or University Degree                                       -4.31928528
## EducationCSEs or equivalent                                                 -0.47619315
## EducationNational Vocational Qualification or equivalent                     0.17479263
## EducationNone of the above                                                  -0.60485514
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.47653881
## EducationOther professional qualifications                                   0.27805632
## Income                                                                      -1.17278035
## Average_time_outdoors                                                       -0.11768312
## Summed_PA_min                                                               -0.01508839
## Smoking                                                                     -6.30573414
## Disability                                                                  -3.41870092
## Deprivation_Index                                                           -0.05833024
## Population_density                                                          -3.02413118
## Natural_environment_1000m_10pcnt:Sex                                        -1.29247656
##                                                                                   97.5 %
## (Intercept)                                                                804.360070102
## Natural_environment_1000m_10pcnt                                             1.129989863
## Sex                                                                         29.551495783
## Age                                                                        -35.759316733
## BMI                                                                         -4.590519289
## EducationCollege or University Degree                                        0.094433291
## EducationCSEs or equivalent                                                  8.711678867
## EducationNational Vocational Qualification or equivalent                     8.137022797
## EducationNone of the above                                                   8.095132088
## EducationO levels/General Certificate of Secondary Education or equivalent   3.707791630
## EducationOther professional qualifications                                   8.365520679
## Income                                                                       0.281723306
## Average_time_outdoors                                                        0.901795751
## Summed_PA_min                                                                0.002407306
## Smoking                                                                     -3.853481646
## Disability                                                                   0.069097778
## Deprivation_Index                                                            0.042799085
## Population_density                                                           0.199125324
## Natural_environment_1000m_10pcnt:Sex                                         0.010529987

Moderation by sex: White Matter (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -149.646, -26.207, -1.375, 24.647, 178.858
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                705.606341
## Natural_environment_1000m_10pcnt                                             0.701941
## Sex                                                                         -8.778645
## Age                                                                        -17.115958
## BMI                                                                          0.172456
## EducationCollege or University Degree                                       -2.820013
## EducationCSEs or equivalent                                                  1.364160
## EducationNational Vocational Qualification or equivalent                     0.312530
## EducationNone of the above                                                   2.313335
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.803981
## EducationOther professional qualifications                                   1.229314
## Income                                                                      -0.530078
## Average_time_outdoors                                                        0.078614
## Summed_PA_min                                                                0.001807
## Smoking                                                                     -1.243741
## Disability                                                                  -1.288499
## Deprivation_Index                                                           -0.047666
## Population_density                                                          -0.838126
## Natural_environment_1000m_10pcnt:Sex                                        -0.235150
##                                                                            Std. Error
## (Intercept)                                                                  2.342729
## Natural_environment_1000m_10pcnt                                             0.247619
## Sex                                                                          1.934514
## Age                                                                          0.596026
## BMI                                                                          0.497057
## EducationCollege or University Degree                                        1.235917
## EducationCSEs or equivalent                                                  2.572763
## EducationNational Vocational Qualification or equivalent                     2.229562
## EducationNone of the above                                                   2.436146
## EducationO levels/General Certificate of Secondary Education or equivalent   1.451702
## EducationOther professional qualifications                                   2.264629
## Income                                                                       0.407286
## Average_time_outdoors                                                        0.285472
## Summed_PA_min                                                                0.004899
## Smoking                                                                      0.686673
## Disability                                                                   0.976644
## Deprivation_Index                                                            0.028318
## Population_density                                                           0.902567
## Natural_environment_1000m_10pcnt:Sex                                         0.364864
##                                                                            t value
## (Intercept)                                                                301.190
## Natural_environment_1000m_10pcnt                                             2.835
## Sex                                                                         -4.538
## Age                                                                        -28.717
## BMI                                                                          0.347
## EducationCollege or University Degree                                       -2.282
## EducationCSEs or equivalent                                                  0.530
## EducationNational Vocational Qualification or equivalent                     0.140
## EducationNone of the above                                                   0.950
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.554
## EducationOther professional qualifications                                   0.543
## Income                                                                      -1.301
## Average_time_outdoors                                                        0.275
## Summed_PA_min                                                                0.369
## Smoking                                                                     -1.811
## Disability                                                                  -1.319
## Deprivation_Index                                                           -1.683
## Population_density                                                          -0.929
## Natural_environment_1000m_10pcnt:Sex                                        -0.644
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.0046
## Sex                                                                        5.75e-06
## Age                                                                         < 2e-16
## BMI                                                                          0.7286
## EducationCollege or University Degree                                        0.0225
## EducationCSEs or equivalent                                                  0.5960
## EducationNational Vocational Qualification or equivalent                     0.8885
## EducationNone of the above                                                   0.3423
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5797
## EducationOther professional qualifications                                   0.5873
## Income                                                                       0.1931
## Average_time_outdoors                                                        0.7830
## Summed_PA_min                                                                0.7123
## Smoking                                                                      0.0701
## Disability                                                                   0.1871
## Deprivation_Index                                                            0.0924
## Population_density                                                           0.3531
## Natural_environment_1000m_10pcnt:Sex                                         0.5193
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                           ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    .  
## Disability                                                                    
## Deprivation_Index                                                          .  
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.78 on 9149 degrees of freedom
## Multiple R-squared:  0.0988, Adjusted R-squared:  0.09703 
## F-statistic: 55.73 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                701.014068427
## Natural_environment_1000m_10pcnt                                             0.216552023
## Sex                                                                        -12.570724199
## Age                                                                        -18.284302156
## BMI                                                                         -0.801887362
## EducationCollege or University Degree                                       -5.242686954
## EducationCSEs or equivalent                                                 -3.679029536
## EducationNational Vocational Qualification or equivalent                    -4.057908715
## EducationNone of the above                                                  -2.462055697
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.649641328
## EducationOther professional qualifications                                  -3.209865035
## Income                                                                      -1.328449643
## Average_time_outdoors                                                       -0.480974562
## Summed_PA_min                                                               -0.007796741
## Smoking                                                                     -2.589773200
## Disability                                                                  -3.202939072
## Deprivation_Index                                                           -0.103175633
## Population_density                                                          -2.607359581
## Natural_environment_1000m_10pcnt:Sex                                        -0.950365729
##                                                                                   97.5 %
## (Intercept)                                                                710.198613272
## Natural_environment_1000m_10pcnt                                             1.187330187
## Sex                                                                         -4.986566316
## Age                                                                        -15.947613671
## BMI                                                                          1.146798390
## EducationCollege or University Degree                                       -0.397339088
## EducationCSEs or equivalent                                                  6.407348948
## EducationNational Vocational Qualification or equivalent                     4.682969135
## EducationNone of the above                                                   7.088726440
## EducationO levels/General Certificate of Secondary Education or equivalent   2.041678584
## EducationOther professional qualifications                                   5.668493988
## Income                                                                       0.268293799
## Average_time_outdoors                                                        0.638201862
## Summed_PA_min                                                                0.011409907
## Smoking                                                                      0.102291594
## Disability                                                                   0.625940747
## Deprivation_Index                                                            0.007843396
## Population_density                                                           0.931107760
## Natural_environment_1000m_10pcnt:Sex                                         0.480065302

Moderation by sex: Average hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.6031, -0.3114, 0.0217, 0.3391, 5.6354
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.984e+00
## Natural_environment_1000m_10pcnt                                            2.036e-03
## Sex                                                                         3.010e-01
## Age                                                                        -2.160e-01
## BMI                                                                        -1.349e-02
## EducationCollege or University Degree                                       3.950e-02
## EducationCSEs or equivalent                                                 5.854e-02
## EducationNational Vocational Qualification or equivalent                    6.108e-02
## EducationNone of the above                                                  5.807e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  4.393e-02
## EducationOther professional qualifications                                  2.975e-02
## Income                                                                     -1.502e-03
## Average_time_outdoors                                                       2.482e-03
## Summed_PA_min                                                              -1.798e-05
## Smoking                                                                    -3.819e-02
## Disability                                                                 -3.065e-02
## Deprivation_Index                                                           1.611e-04
## Population_density                                                         -1.878e-02
## Natural_environment_1000m_10pcnt:Sex                                       -3.386e-03
##                                                                            Std. Error
## (Intercept)                                                                 3.186e-02
## Natural_environment_1000m_10pcnt                                            3.367e-03
## Sex                                                                         2.630e-02
## Age                                                                         8.103e-03
## BMI                                                                         6.759e-03
## EducationCollege or University Degree                                       1.681e-02
## EducationCSEs or equivalent                                                 3.502e-02
## EducationNational Vocational Qualification or equivalent                    3.031e-02
## EducationNone of the above                                                  3.312e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.974e-02
## EducationOther professional qualifications                                  3.079e-02
## Income                                                                      5.538e-03
## Average_time_outdoors                                                       3.881e-03
## Summed_PA_min                                                               6.660e-05
## Smoking                                                                     9.336e-03
## Disability                                                                  1.328e-02
## Deprivation_Index                                                           3.850e-04
## Population_density                                                          1.227e-02
## Natural_environment_1000m_10pcnt:Sex                                        4.961e-03
##                                                                            t value
## (Intercept)                                                                156.432
## Natural_environment_1000m_10pcnt                                             0.605
## Sex                                                                         11.444
## Age                                                                        -26.654
## BMI                                                                         -1.996
## EducationCollege or University Degree                                        2.350
## EducationCSEs or equivalent                                                  1.671
## EducationNational Vocational Qualification or equivalent                     2.015
## EducationNone of the above                                                   1.753
## EducationO levels/General Certificate of Secondary Education or equivalent   2.225
## EducationOther professional qualifications                                   0.966
## Income                                                                      -0.271
## Average_time_outdoors                                                        0.639
## Summed_PA_min                                                               -0.270
## Smoking                                                                     -4.090
## Disability                                                                  -2.307
## Deprivation_Index                                                            0.418
## Population_density                                                          -1.530
## Natural_environment_1000m_10pcnt:Sex                                        -0.683
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_1000m_10pcnt                                             0.5454
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0460
## EducationCollege or University Degree                                        0.0188
## EducationCSEs or equivalent                                                  0.0947
## EducationNational Vocational Qualification or equivalent                     0.0439
## EducationNone of the above                                                   0.0796
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0261
## EducationOther professional qualifications                                   0.3339
## Income                                                                       0.7862
## Average_time_outdoors                                                        0.5226
## Summed_PA_min                                                                0.7872
## Smoking                                                                    4.35e-05
## Disability                                                                   0.0211
## Deprivation_Index                                                            0.6756
## Population_density                                                           0.1259
## Natural_environment_1000m_10pcnt:Sex                                         0.4949
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_1000m_10pcnt                                              
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_1000m_10pcnt:Sex                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5271 on 9143 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1654, Adjusted R-squared:  0.1638 
## F-statistic: 100.7 on 18 and 9143 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.9212133741
## Natural_environment_1000m_10pcnt                                           -0.0045638134
## Sex                                                                         0.2494506137
## Age                                                                        -0.2318522290
## BMI                                                                        -0.0267375773
## EducationCollege or University Degree                                       0.0065582776
## EducationCSEs or equivalent                                                -0.0101122902
## EducationNational Vocational Qualification or equivalent                    0.0016660427
## EducationNone of the above                                                 -0.0068479230
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0052351232
## EducationOther professional qualifications                                 -0.0306003029
## Income                                                                     -0.0123588857
## Average_time_outdoors                                                      -0.0051261261
## Summed_PA_min                                                              -0.0001485358
## Smoking                                                                    -0.0564880397
## Disability                                                                 -0.0566904678
## Deprivation_Index                                                          -0.0005936596
## Population_density                                                         -0.0428354182
## Natural_environment_1000m_10pcnt:Sex                                       -0.0131099714
##                                                                                   97.5 %
## (Intercept)                                                                 5.0461122823
## Natural_environment_1000m_10pcnt                                            0.0086362342
## Sex                                                                         0.3525724747
## Age                                                                        -0.2000863527
## BMI                                                                        -0.0002407107
## EducationCollege or University Degree                                       0.0724512323
## EducationCSEs or equivalent                                                 0.1271963257
## EducationNational Vocational Qualification or equivalent                    0.1204974966
## EducationNone of the above                                                  0.1229935471
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0826266676
## EducationOther professional qualifications                                  0.0901013514
## Income                                                                      0.0093541803
## Average_time_outdoors                                                       0.0100893398
## Summed_PA_min                                                               0.0001125837
## Smoking                                                                    -0.0198853766
## Disability                                                                 -0.0046114570
## Deprivation_Index                                                           0.0009158887
## Population_density                                                          0.0052733226
## Natural_environment_1000m_10pcnt:Sex                                        0.0063380776

10.2.2) 300m natural environment buffer

Association of natural environment with grey matter volume (300m buffer AND restricted sample)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -173.474, -22.799, 0.063, 23.995, 178.485
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                801.284374
## Natural_environment_300m_10pcnt                                              0.544547
## Age                                                                        -36.797945
## Sex                                                                         22.970982
## BMI                                                                         -5.477293
## EducationCollege or University Degree                                       -2.205594
## EducationCSEs or equivalent                                                  4.207517
## EducationNational Vocational Qualification or equivalent                     4.167304
## EducationNone of the above                                                   3.659851
## EducationO levels/General Certificate of Secondary Education or equivalent   1.084738
## EducationOther professional qualifications                                   4.296565
## Income                                                                      -0.476263
## Average_time_outdoors                                                        0.391758
## Summed_PA_min                                                               -0.006188
## Smoking                                                                     -5.108899
## Disability                                                                  -1.698879
## Deprivation_Index                                                           -0.007306
## Population_density                                                          -1.170728
##                                                                            Std. Error
## (Intercept)                                                                  2.088310
## Natural_environment_300m_10pcnt                                              0.202435
## Age                                                                          0.542985
## Sex                                                                          0.771134
## BMI                                                                          0.452862
## EducationCollege or University Degree                                        1.125216
## EducationCSEs or equivalent                                                  2.343989
## EducationNational Vocational Qualification or equivalent                     2.031614
## EducationNone of the above                                                   2.219588
## EducationO levels/General Certificate of Secondary Education or equivalent   1.322717
## EducationOther professional qualifications                                   2.063525
## Income                                                                       0.370997
## Average_time_outdoors                                                        0.260127
## Summed_PA_min                                                                0.004463
## Smoking                                                                      0.625281
## Disability                                                                   0.889824
## Deprivation_Index                                                            0.025802
## Population_density                                                           0.809918
##                                                                            t value
## (Intercept)                                                                383.700
## Natural_environment_300m_10pcnt                                              2.690
## Age                                                                        -67.770
## Sex                                                                         29.789
## BMI                                                                        -12.095
## EducationCollege or University Degree                                       -1.960
## EducationCSEs or equivalent                                                  1.795
## EducationNational Vocational Qualification or equivalent                     2.051
## EducationNone of the above                                                   1.649
## EducationO levels/General Certificate of Secondary Education or equivalent   0.820
## EducationOther professional qualifications                                   2.082
## Income                                                                      -1.284
## Average_time_outdoors                                                        1.506
## Summed_PA_min                                                               -1.387
## Smoking                                                                     -8.171
## Disability                                                                  -1.909
## Deprivation_Index                                                           -0.283
## Population_density                                                          -1.445
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.00716
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.05001
## EducationCSEs or equivalent                                                 0.07268
## EducationNational Vocational Qualification or equivalent                    0.04027
## EducationNone of the above                                                  0.09921
## EducationO levels/General Certificate of Secondary Education or equivalent  0.41219
## EducationOther professional qualifications                                  0.03736
## Income                                                                      0.19927
## Average_time_outdoors                                                       0.13210
## Summed_PA_min                                                               0.16561
## Smoking                                                                    3.48e-16
## Disability                                                                  0.05626
## Deprivation_Index                                                           0.77707
## Population_density                                                          0.14835
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ** 
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      .  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.33 on 9150 degrees of freedom
## Multiple R-squared:  0.4513, Adjusted R-squared:  0.4503 
## F-statistic: 442.7 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                797.19081984
## Natural_environment_300m_10pcnt                                              0.14772907
## Age                                                                        -37.86231713
## Sex                                                                         21.45938670
## BMI                                                                         -6.36500367
## EducationCollege or University Degree                                       -4.41126804
## EducationCSEs or equivalent                                                 -0.38722562
## EducationNational Vocational Qualification or equivalent                     0.18488720
## EducationNone of the above                                                  -0.69103729
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.50808339
## EducationOther professional qualifications                                   0.25159420
## Income                                                                      -1.20350029
## Average_time_outdoors                                                       -0.11814966
## Summed_PA_min                                                               -0.01493673
## Smoking                                                                     -6.33458981
## Disability                                                                  -3.44313206
## Deprivation_Index                                                           -0.05788370
## Population_density                                                          -2.75834882
##                                                                                   97.5 %
## (Intercept)                                                                 8.053779e+02
## Natural_environment_300m_10pcnt                                             9.413641e-01
## Age                                                                        -3.573357e+01
## Sex                                                                         2.448258e+01
## BMI                                                                        -4.589582e+00
## EducationCollege or University Degree                                       8.011626e-05
## EducationCSEs or equivalent                                                 8.802259e+00
## EducationNational Vocational Qualification or equivalent                    8.149720e+00
## EducationNone of the above                                                  8.010739e+00
## EducationO levels/General Certificate of Secondary Education or equivalent  3.677559e+00
## EducationOther professional qualifications                                  8.341535e+00
## Income                                                                      2.509746e-01
## Average_time_outdoors                                                       9.016654e-01
## Summed_PA_min                                                               2.560260e-03
## Smoking                                                                    -3.883209e+00
## Disability                                                                  4.537350e-02
## Deprivation_Index                                                           4.327212e-02
## Population_density                                                          4.168928e-01

Association of natural environment with white matter volume (300m buffer AND restricted sample)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -147.224, -26.146, -1.281, 24.649, 180.814
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                706.768903
## Natural_environment_300m_10pcnt                                              0.506817
## Age                                                                        -17.094234
## Sex                                                                         -9.974378
## BMI                                                                          0.178859
## EducationCollege or University Degree                                       -2.921977
## EducationCSEs or equivalent                                                  1.431996
## EducationNational Vocational Qualification or equivalent                     0.318296
## EducationNone of the above                                                   2.274281
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.806608
## EducationOther professional qualifications                                   1.217132
## Income                                                                      -0.564615
## Average_time_outdoors                                                        0.073719
## Summed_PA_min                                                                0.001985
## Smoking                                                                     -1.282783
## Disability                                                                  -1.317487
## Deprivation_Index                                                           -0.047230
## Population_density                                                          -0.458186
##                                                                            Std. Error
## (Intercept)                                                                  2.292230
## Natural_environment_300m_10pcnt                                              0.222202
## Age                                                                          0.596006
## Sex                                                                          0.846434
## BMI                                                                          0.497083
## EducationCollege or University Degree                                        1.235091
## EducationCSEs or equivalent                                                  2.572875
## EducationNational Vocational Qualification or equivalent                     2.229997
## EducationNone of the above                                                   2.436327
## EducationO levels/General Certificate of Secondary Education or equivalent   1.451878
## EducationOther professional qualifications                                   2.265025
## Income                                                                       0.407224
## Average_time_outdoors                                                        0.285528
## Summed_PA_min                                                                0.004899
## Smoking                                                                      0.686338
## Disability                                                                   0.976713
## Deprivation_Index                                                            0.028322
## Population_density                                                           0.889005
##                                                                            t value
## (Intercept)                                                                308.333
## Natural_environment_300m_10pcnt                                              2.281
## Age                                                                        -28.681
## Sex                                                                        -11.784
## BMI                                                                          0.360
## EducationCollege or University Degree                                       -2.366
## EducationCSEs or equivalent                                                  0.557
## EducationNational Vocational Qualification or equivalent                     0.143
## EducationNone of the above                                                   0.933
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.556
## EducationOther professional qualifications                                   0.537
## Income                                                                      -1.386
## Average_time_outdoors                                                        0.258
## Summed_PA_min                                                                0.405
## Smoking                                                                     -1.869
## Disability                                                                  -1.349
## Deprivation_Index                                                           -1.668
## Population_density                                                          -0.515
##                                                                            Pr(>|t|)
## (Intercept)                                                                  <2e-16
## Natural_environment_300m_10pcnt                                              0.0226
## Age                                                                          <2e-16
## Sex                                                                          <2e-16
## BMI                                                                          0.7190
## EducationCollege or University Degree                                        0.0180
## EducationCSEs or equivalent                                                  0.5778
## EducationNational Vocational Qualification or equivalent                     0.8865
## EducationNone of the above                                                   0.3506
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5785
## EducationOther professional qualifications                                   0.5910
## Income                                                                       0.1656
## Average_time_outdoors                                                        0.7963
## Summed_PA_min                                                                0.6854
## Smoking                                                                      0.0617
## Disability                                                                   0.1774
## Deprivation_Index                                                            0.0954
## Population_density                                                           0.6063
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    .  
## Disability                                                                    
## Deprivation_Index                                                          .  
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.78 on 9150 degrees of freedom
## Multiple R-squared:  0.09849,    Adjusted R-squared:  0.09681 
## F-statistic:  58.8 on 17 and 9150 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                702.275621620
## Natural_environment_300m_10pcnt                                              0.071251155
## Age                                                                        -18.262539853
## Sex                                                                        -11.633577650
## BMI                                                                         -0.795535070
## EducationCollege or University Degree                                       -5.343030350
## EducationCSEs or equivalent                                                 -3.611413618
## EducationNational Vocational Qualification or equivalent                    -4.052996267
## EducationNone of the above                                                  -2.501462729
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.652612678
## EducationOther professional qualifications                                  -3.222821280
## Income                                                                      -1.362865887
## Average_time_outdoors                                                       -0.485979774
## Summed_PA_min                                                               -0.007617973
## Smoking                                                                     -2.628159710
## Disability                                                                  -3.232062257
## Deprivation_Index                                                           -0.102747154
## Population_density                                                          -2.200835276
##                                                                                   97.5 %
## (Intercept)                                                                711.262185051
## Natural_environment_300m_10pcnt                                              0.942383040
## Age                                                                        -15.925928364
## Sex                                                                         -8.315177903
## BMI                                                                          1.153252494
## EducationCollege or University Degree                                       -0.500922723
## EducationCSEs or equivalent                                                  6.475406343
## EducationNational Vocational Qualification or equivalent                     4.689587302
## EducationNone of the above                                                   7.050025314
## EducationO levels/General Certificate of Secondary Education or equivalent   2.039397659
## EducationOther professional qualifications                                   5.657086251
## Income                                                                       0.233635588
## Average_time_outdoors                                                        0.633418167
## Summed_PA_min                                                                0.011587560
## Smoking                                                                      0.062593478
## Disability                                                                   0.597089011
## Deprivation_Index                                                            0.008286333
## Population_density                                                           1.284462404

Association of natural environment with average hippocampal volume (300m buffer AND restricted sample)

Full adjusted model (Covariates: Age, Sex, BMI, Education, Income, Average time spent outdoors, Physical activity minutes, Smoking status, Disability status, Townsend Deprivation Index, and Population Density)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + BMI + Education + Income + Average_time_outdoors + Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5909, -0.31, 0.0207, 0.3398, 5.6411
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.989e+00
## Natural_environment_300m_10pcnt                                            -3.155e-03
## Age                                                                        -2.158e-01
## Sex                                                                         2.845e-01
## BMI                                                                        -1.332e-02
## EducationCollege or University Degree                                       3.877e-02
## EducationCSEs or equivalent                                                 5.907e-02
## EducationNational Vocational Qualification or equivalent                    6.225e-02
## EducationNone of the above                                                  5.840e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  4.458e-02
## EducationOther professional qualifications                                  3.039e-02
## Income                                                                     -1.491e-03
## Average_time_outdoors                                                       2.651e-03
## Summed_PA_min                                                              -1.651e-05
## Smoking                                                                    -3.873e-02
## Disability                                                                 -3.067e-02
## Deprivation_Index                                                           1.593e-04
## Population_density                                                         -5.521e-03
##                                                                            Std. Error
## (Intercept)                                                                 3.117e-02
## Natural_environment_300m_10pcnt                                             3.022e-03
## Age                                                                         8.101e-03
## Sex                                                                         1.151e-02
## BMI                                                                         6.758e-03
## EducationCollege or University Degree                                       1.679e-02
## EducationCSEs or equivalent                                                 3.502e-02
## EducationNational Vocational Qualification or equivalent                    3.031e-02
## EducationNone of the above                                                  3.312e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.974e-02
## EducationOther professional qualifications                                  3.079e-02
## Income                                                                      5.537e-03
## Average_time_outdoors                                                       3.881e-03
## Summed_PA_min                                                               6.659e-05
## Smoking                                                                     9.330e-03
## Disability                                                                  1.328e-02
## Deprivation_Index                                                           3.850e-04
## Population_density                                                          1.209e-02
##                                                                            t value
## (Intercept)                                                                160.087
## Natural_environment_300m_10pcnt                                             -1.044
## Age                                                                        -26.637
## Sex                                                                         24.722
## BMI                                                                         -1.970
## EducationCollege or University Degree                                        2.309
## EducationCSEs or equivalent                                                  1.687
## EducationNational Vocational Qualification or equivalent                     2.054
## EducationNone of the above                                                   1.764
## EducationO levels/General Certificate of Secondary Education or equivalent   2.259
## EducationOther professional qualifications                                   0.987
## Income                                                                      -0.269
## Average_time_outdoors                                                        0.683
## Summed_PA_min                                                               -0.248
## Smoking                                                                     -4.151
## Disability                                                                  -2.309
## Deprivation_Index                                                            0.414
## Population_density                                                          -0.457
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.2965
## Age                                                                         < 2e-16
## Sex                                                                         < 2e-16
## BMI                                                                          0.0488
## EducationCollege or University Degree                                        0.0210
## EducationCSEs or equivalent                                                  0.0916
## EducationNational Vocational Qualification or equivalent                     0.0400
## EducationNone of the above                                                   0.0778
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0239
## EducationOther professional qualifications                                   0.3236
## Income                                                                       0.7877
## Average_time_outdoors                                                        0.4945
## Summed_PA_min                                                                0.8042
## Smoking                                                                    3.34e-05
## Disability                                                                   0.0210
## Deprivation_Index                                                            0.6791
## Population_density                                                           0.6479
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Age                                                                        ***
## Sex                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5271 on 9144 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1654, Adjusted R-squared:  0.1639 
## F-statistic: 106.6 on 17 and 9144 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.9280601082
## Natural_environment_300m_10pcnt                                            -0.0090797693
## Age                                                                        -0.2316576200
## Sex                                                                         0.2619191678
## BMI                                                                        -0.0265622678
## EducationCollege or University Degree                                       0.0058560794
## EducationCSEs or equivalent                                                -0.0095700700
## EducationNational Vocational Qualification or equivalent                    0.0028299337
## EducationNone of the above                                                 -0.0065127181
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0058906965
## EducationOther professional qualifications                                 -0.0299556148
## Income                                                                     -0.0123437088
## Average_time_outdoors                                                      -0.0049562550
## Summed_PA_min                                                              -0.0001470387
## Smoking                                                                    -0.0570153645
## Disability                                                                 -0.0567037078
## Deprivation_Index                                                          -0.0005954406
## Population_density                                                         -0.0292155116
##                                                                                   97.5 %
## (Intercept)                                                                 5.050242e+00
## Natural_environment_300m_10pcnt                                             2.768999e-03
## Age                                                                        -1.998988e-01
## Sex                                                                         3.070315e-01
## BMI                                                                        -6.909505e-05
## EducationCollege or University Degree                                       7.169181e-02
## EducationCSEs or equivalent                                                 1.277172e-01
## EducationNational Vocational Qualification or equivalent                    1.216623e-01
## EducationNone of the above                                                  1.233141e-01
## EducationO levels/General Certificate of Secondary Education or equivalent  8.327748e-02
## EducationOther professional qualifications                                  9.074441e-02
## Income                                                                      9.361975e-03
## Average_time_outdoors                                                       1.025923e-02
## Summed_PA_min                                                               1.140167e-04
## Smoking                                                                    -2.043764e-02
## Disability                                                                 -4.631261e-03
## Deprivation_Index                                                           9.140226e-04
## Population_density                                                          1.817360e-02

Moderation by sex: Grey Matter [300m buffer AND subset with no address change] (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.651, -22.816, 0.195, 23.873, 179.04
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                801.312406
## Natural_environment_300m_10pcnt                                              0.548074
## Sex                                                                         25.791874
## Age                                                                        -36.782028
## BMI                                                                         -5.479922
## EducationCollege or University Degree                                       -2.205068
## EducationCSEs or equivalent                                                  4.192652
## EducationNational Vocational Qualification or equivalent                     4.126656
## EducationNone of the above                                                   3.714939
## EducationO levels/General Certificate of Secondary Education or equivalent   1.109640
## EducationOther professional qualifications                                   4.343849
## Income                                                                      -0.483926
## Average_time_outdoors                                                        0.372832
## Summed_PA_min                                                               -0.005994
## Smoking                                                                     -5.101869
## Disability                                                                  -1.715359
## Deprivation_Index                                                           -0.007711
## Population_density                                                          -1.183656
## Natural_environment_300m_10pcnt:Sex                                         -0.745220
##                                                                            Std. Error
## (Intercept)                                                                  2.087766
## Natural_environment_300m_10pcnt                                              0.202384
## Sex                                                                          1.382613
## Age                                                                          0.542874
## BMI                                                                          0.452739
## EducationCollege or University Degree                                        1.124906
## EducationCSEs or equivalent                                                  2.343352
## EducationNational Vocational Qualification or equivalent                     2.031122
## EducationNone of the above                                                   2.219090
## EducationO levels/General Certificate of Secondary Education or equivalent   1.322392
## EducationOther professional qualifications                                   2.063047
## Income                                                                       0.370908
## Average_time_outdoors                                                        0.260170
## Summed_PA_min                                                                0.004462
## Smoking                                                                      0.625115
## Disability                                                                   0.889604
## Deprivation_Index                                                            0.025796
## Population_density                                                           0.809712
## Natural_environment_300m_10pcnt:Sex                                          0.303207
##                                                                            t value
## (Intercept)                                                                383.813
## Natural_environment_300m_10pcnt                                              2.708
## Sex                                                                         18.654
## Age                                                                        -67.754
## BMI                                                                        -12.104
## EducationCollege or University Degree                                       -1.960
## EducationCSEs or equivalent                                                  1.789
## EducationNational Vocational Qualification or equivalent                     2.032
## EducationNone of the above                                                   1.674
## EducationO levels/General Certificate of Secondary Education or equivalent   0.839
## EducationOther professional qualifications                                   2.106
## Income                                                                      -1.305
## Average_time_outdoors                                                        1.433
## Summed_PA_min                                                               -1.343
## Smoking                                                                     -8.161
## Disability                                                                  -1.928
## Deprivation_Index                                                           -0.299
## Population_density                                                          -1.462
## Natural_environment_300m_10pcnt:Sex                                         -2.458
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                             0.00678
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                         < 2e-16
## EducationCollege or University Degree                                       0.05000
## EducationCSEs or equivalent                                                 0.07362
## EducationNational Vocational Qualification or equivalent                    0.04221
## EducationNone of the above                                                  0.09415
## EducationO levels/General Certificate of Secondary Education or equivalent  0.40143
## EducationOther professional qualifications                                  0.03527
## Income                                                                      0.19203
## Average_time_outdoors                                                       0.15188
## Summed_PA_min                                                               0.17923
## Smoking                                                                    3.75e-16
## Disability                                                                  0.05386
## Deprivation_Index                                                           0.76501
## Population_density                                                          0.14382
## Natural_environment_300m_10pcnt:Sex                                         0.01400
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            ** 
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        ***
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                 *  
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 .  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                        *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.32 on 9149 degrees of freedom
## Multiple R-squared:  0.4517, Adjusted R-squared:  0.4506 
## F-statistic: 418.7 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                   2.5 %
## (Intercept)                                                                797.21991747
## Natural_environment_300m_10pcnt                                              0.15135611
## Sex                                                                         23.08164328
## Age                                                                        -37.84618213
## BMI                                                                         -6.36739070
## EducationCollege or University Degree                                       -4.41013531
## EducationCSEs or equivalent                                                 -0.40084037
## EducationNational Vocational Qualification or equivalent                     0.14520353
## EducationNone of the above                                                  -0.63497368
## EducationO levels/General Certificate of Secondary Education or equivalent  -1.48254400
## EducationOther professional qualifications                                   0.29981636
## Income                                                                      -1.21098928
## Average_time_outdoors                                                       -0.13715827
## Summed_PA_min                                                               -0.01474161
## Smoking                                                                     -6.32723501
## Disability                                                                  -3.45918063
## Deprivation_Index                                                           -0.05827589
## Population_density                                                          -2.77087341
## Natural_environment_300m_10pcnt:Sex                                         -1.33957389
##                                                                                   97.5 %
## (Intercept)                                                                 8.054049e+02
## Natural_environment_300m_10pcnt                                             9.447926e-01
## Sex                                                                         2.850210e+01
## Age                                                                        -3.571787e+01
## BMI                                                                        -4.592453e+00
## EducationCollege or University Degree                                      -1.605685e-06
## EducationCSEs or equivalent                                                 8.786145e+00
## EducationNational Vocational Qualification or equivalent                    8.108108e+00
## EducationNone of the above                                                  8.064851e+00
## EducationO levels/General Certificate of Secondary Education or equivalent  3.701823e+00
## EducationOther professional qualifications                                  8.387881e+00
## Income                                                                      2.431365e-01
## Average_time_outdoors                                                       8.828228e-01
## Summed_PA_min                                                               2.753299e-03
## Smoking                                                                    -3.876504e+00
## Disability                                                                  2.846354e-02
## Deprivation_Index                                                           4.285414e-02
## Population_density                                                          4.035610e-01
## Natural_environment_300m_10pcnt:Sex                                        -1.508651e-01

Moderation by sex: White Matter [300m buffer AND subset with no address change] (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -147.039, -26.081, -1.335, 24.673, 180.656
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                706.776338
## Natural_environment_300m_10pcnt                                              0.507753
## Sex                                                                         -9.226252
## Age                                                                        -17.090013
## BMI                                                                          0.178161
## EducationCollege or University Degree                                       -2.921837
## EducationCSEs or equivalent                                                  1.428054
## EducationNational Vocational Qualification or equivalent                     0.307515
## EducationNone of the above                                                   2.288891
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.800003
## EducationOther professional qualifications                                   1.229673
## Income                                                                      -0.566648
## Average_time_outdoors                                                        0.068700
## Summed_PA_min                                                                0.002036
## Smoking                                                                     -1.280919
## Disability                                                                  -1.321857
## Deprivation_Index                                                           -0.047338
## Population_density                                                          -0.461615
## Natural_environment_300m_10pcnt:Sex                                         -0.197639
##                                                                            Std. Error
## (Intercept)                                                                  2.292345
## Natural_environment_300m_10pcnt                                              0.222216
## Sex                                                                          1.518094
## Age                                                                          0.596070
## BMI                                                                          0.497102
## EducationCollege or University Degree                                        1.235135
## EducationCSEs or equivalent                                                  2.572975
## EducationNational Vocational Qualification or equivalent                     2.230150
## EducationNone of the above                                                   2.436537
## EducationO levels/General Certificate of Secondary Education or equivalent   1.451972
## EducationOther professional qualifications                                   2.265203
## Income                                                                       0.407253
## Average_time_outdoors                                                        0.285663
## Summed_PA_min                                                                0.004900
## Smoking                                                                      0.686370
## Disability                                                                   0.976775
## Deprivation_Index                                                            0.028323
## Population_density                                                           0.889055
## Natural_environment_300m_10pcnt:Sex                                          0.332919
##                                                                            t value
## (Intercept)                                                                308.320
## Natural_environment_300m_10pcnt                                              2.285
## Sex                                                                         -6.078
## Age                                                                        -28.671
## BMI                                                                          0.358
## EducationCollege or University Degree                                       -2.366
## EducationCSEs or equivalent                                                  0.555
## EducationNational Vocational Qualification or equivalent                     0.138
## EducationNone of the above                                                   0.939
## EducationO levels/General Certificate of Secondary Education or equivalent  -0.551
## EducationOther professional qualifications                                   0.543
## Income                                                                      -1.391
## Average_time_outdoors                                                        0.240
## Summed_PA_min                                                                0.416
## Smoking                                                                     -1.866
## Disability                                                                  -1.353
## Deprivation_Index                                                           -1.671
## Population_density                                                          -0.519
## Natural_environment_300m_10pcnt:Sex                                         -0.594
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.0223
## Sex                                                                        1.27e-09
## Age                                                                         < 2e-16
## BMI                                                                          0.7201
## EducationCollege or University Degree                                        0.0180
## EducationCSEs or equivalent                                                  0.5789
## EducationNational Vocational Qualification or equivalent                     0.8903
## EducationNone of the above                                                   0.3475
## EducationO levels/General Certificate of Secondary Education or equivalent   0.5817
## EducationOther professional qualifications                                   0.5872
## Income                                                                       0.1641
## Average_time_outdoors                                                        0.8100
## Summed_PA_min                                                                0.6777
## Smoking                                                                      0.0620
## Disability                                                                   0.1760
## Deprivation_Index                                                            0.0947
## Population_density                                                           0.6036
## Natural_environment_300m_10pcnt:Sex                                          0.5528
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                            *  
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                           
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                   
## EducationNational Vocational Qualification or equivalent                      
## EducationNone of the above                                                    
## EducationO levels/General Certificate of Secondary Education or equivalent    
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    .  
## Disability                                                                    
## Deprivation_Index                                                          .  
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.78 on 9149 degrees of freedom
## Multiple R-squared:  0.09852,    Adjusted R-squared:  0.09675 
## F-statistic: 55.55 on 18 and 9149 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                702.282829735
## Natural_environment_300m_10pcnt                                              0.072160375
## Sex                                                                        -12.202056441
## Age                                                                        -18.258442854
## BMI                                                                         -0.796269509
## EducationCollege or University Degree                                       -5.342976737
## EducationCSEs or equivalent                                                 -3.615551159
## EducationNational Vocational Qualification or equivalent                    -4.064076187
## EducationNone of the above                                                  -2.487265714
## EducationO levels/General Certificate of Secondary Education or equivalent  -3.646192845
## EducationOther professional qualifications                                  -3.210631316
## Income                                                                      -1.364954789
## Average_time_outdoors                                                       -0.491264134
## Summed_PA_min                                                               -0.007568345
## Smoking                                                                     -2.626356961
## Disability                                                                  -3.236554869
## Deprivation_Index                                                           -0.102857685
## Population_density                                                          -2.204362418
## Natural_environment_300m_10pcnt:Sex                                         -0.850233473
##                                                                                  97.5 %
## (Intercept)                                                                711.26984542
## Natural_environment_300m_10pcnt                                              0.94334501
## Sex                                                                         -6.25044829
## Age                                                                        -15.92158234
## BMI                                                                          1.15259249
## EducationCollege or University Degree                                       -0.50069760
## EducationCSEs or equivalent                                                  6.47165950
## EducationNational Vocational Qualification or equivalent                     4.67910674
## EducationNone of the above                                                   7.06504774
## EducationO levels/General Certificate of Secondary Education or equivalent   2.04618608
## EducationOther professional qualifications                                   5.66997673
## Income                                                                       0.23165962
## Average_time_outdoors                                                        0.62866406
## Summed_PA_min                                                                0.01164088
## Smoking                                                                      0.06451966
## Disability                                                                   0.59284073
## Deprivation_Index                                                            0.00818200
## Population_density                                                           1.28113220
## Natural_environment_300m_10pcnt:Sex                                          0.45495588

Moderation by sex: Average hippocampal volume [300m buffer AND subset with no address change] (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age  + BMI + Education + Income + 
             Average_time_outdoors + 
             Summed_PA_min + Smoking + Disability + Deprivation_Index + Population_density, NoHomeChange_T2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + BMI + Education + Income + Average_time_outdoors + 
##     Summed_PA_min + Smoking + Disability + Deprivation_Index + 
##     Population_density, data = NoHomeChange_T2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.583, -0.312, 0.0211, 0.3398, 5.6433
## 
## Coefficients:
##                                                                              Estimate
## (Intercept)                                                                 4.989e+00
## Natural_environment_300m_10pcnt                                            -3.122e-03
## Sex                                                                         3.086e-01
## Age                                                                        -2.156e-01
## BMI                                                                        -1.334e-02
## EducationCollege or University Degree                                       3.878e-02
## EducationCSEs or equivalent                                                 5.890e-02
## EducationNational Vocational Qualification or equivalent                    6.189e-02
## EducationNone of the above                                                  5.887e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  4.480e-02
## EducationOther professional qualifications                                  3.079e-02
## Income                                                                     -1.559e-03
## Average_time_outdoors                                                       2.490e-03
## Summed_PA_min                                                              -1.489e-05
## Smoking                                                                    -3.867e-02
## Disability                                                                 -3.080e-02
## Deprivation_Index                                                           1.561e-04
## Population_density                                                         -5.643e-03
## Natural_environment_300m_10pcnt:Sex                                        -6.370e-03
##                                                                            Std. Error
## (Intercept)                                                                 3.116e-02
## Natural_environment_300m_10pcnt                                             3.022e-03
## Sex                                                                         2.064e-02
## Age                                                                         8.101e-03
## BMI                                                                         6.757e-03
## EducationCollege or University Degree                                       1.679e-02
## EducationCSEs or equivalent                                                 3.502e-02
## EducationNational Vocational Qualification or equivalent                    3.031e-02
## EducationNone of the above                                                  3.312e-02
## EducationO levels/General Certificate of Secondary Education or equivalent  1.974e-02
## EducationOther professional qualifications                                  3.079e-02
## Income                                                                      5.536e-03
## Average_time_outdoors                                                       3.883e-03
## Summed_PA_min                                                               6.659e-05
## Smoking                                                                     9.330e-03
## Disability                                                                  1.328e-02
## Deprivation_Index                                                           3.850e-04
## Population_density                                                          1.209e-02
## Natural_environment_300m_10pcnt:Sex                                         4.526e-03
##                                                                            t value
## (Intercept)                                                                160.101
## Natural_environment_300m_10pcnt                                             -1.033
## Sex                                                                         14.952
## Age                                                                        -26.619
## BMI                                                                         -1.974
## EducationCollege or University Degree                                        2.309
## EducationCSEs or equivalent                                                  1.682
## EducationNational Vocational Qualification or equivalent                     2.042
## EducationNone of the above                                                   1.778
## EducationO levels/General Certificate of Secondary Education or equivalent   2.269
## EducationOther professional qualifications                                   1.000
## Income                                                                      -0.282
## Average_time_outdoors                                                        0.641
## Summed_PA_min                                                               -0.224
## Smoking                                                                     -4.145
## Disability                                                                  -2.319
## Deprivation_Index                                                            0.406
## Population_density                                                          -0.467
## Natural_environment_300m_10pcnt:Sex                                         -1.407
##                                                                            Pr(>|t|)
## (Intercept)                                                                 < 2e-16
## Natural_environment_300m_10pcnt                                              0.3017
## Sex                                                                         < 2e-16
## Age                                                                         < 2e-16
## BMI                                                                          0.0485
## EducationCollege or University Degree                                        0.0209
## EducationCSEs or equivalent                                                  0.0926
## EducationNational Vocational Qualification or equivalent                     0.0412
## EducationNone of the above                                                   0.0755
## EducationO levels/General Certificate of Secondary Education or equivalent   0.0233
## EducationOther professional qualifications                                   0.3172
## Income                                                                       0.7783
## Average_time_outdoors                                                        0.5213
## Summed_PA_min                                                                0.8231
## Smoking                                                                    3.43e-05
## Disability                                                                   0.0204
## Deprivation_Index                                                            0.6851
## Population_density                                                           0.6406
## Natural_environment_300m_10pcnt:Sex                                          0.1593
##                                                                               
## (Intercept)                                                                ***
## Natural_environment_300m_10pcnt                                               
## Sex                                                                        ***
## Age                                                                        ***
## BMI                                                                        *  
## EducationCollege or University Degree                                      *  
## EducationCSEs or equivalent                                                .  
## EducationNational Vocational Qualification or equivalent                   *  
## EducationNone of the above                                                 .  
## EducationO levels/General Certificate of Secondary Education or equivalent *  
## EducationOther professional qualifications                                    
## Income                                                                        
## Average_time_outdoors                                                         
## Summed_PA_min                                                                 
## Smoking                                                                    ***
## Disability                                                                 *  
## Deprivation_Index                                                             
## Population_density                                                            
## Natural_environment_300m_10pcnt:Sex                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.527 on 9143 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.1656, Adjusted R-squared:  0.164 
## F-statistic: 100.8 on 18 and 9143 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                                                                    2.5 %
## (Intercept)                                                                 4.9283168058
## Natural_environment_300m_10pcnt                                            -0.0090457668
## Sex                                                                         0.2681334613
## Age                                                                        -0.2315199562
## BMI                                                                        -0.0265815455
## EducationCollege or University Degree                                       0.0058636907
## EducationCSEs or equivalent                                                -0.0097360493
## EducationNational Vocational Qualification or equivalent                    0.0024791562
## EducationNone of the above                                                 -0.0060474202
## EducationO levels/General Certificate of Secondary Education or equivalent  0.0061036185
## EducationOther professional qualifications                                 -0.0295561764
## Income                                                                     -0.0124115629
## Average_time_outdoors                                                      -0.0051203412
## Summed_PA_min                                                              -0.0001454280
## Smoking                                                                    -0.0569602284
## Disability                                                                 -0.0568365547
## Deprivation_Index                                                          -0.0005985697
## Population_density                                                         -0.0293365091
## Natural_environment_300m_10pcnt:Sex                                        -0.0152428029
##                                                                                   97.5 %
## (Intercept)                                                                 5.050494e+00
## Natural_environment_300m_10pcnt                                             2.802742e-03
## Sex                                                                         3.490486e-01
## Age                                                                        -1.997605e-01
## BMI                                                                        -8.973488e-05
## EducationCollege or University Degree                                       7.169590e-02
## EducationCSEs or equivalent                                                 1.275447e-01
## EducationNational Vocational Qualification or equivalent                    1.213092e-01
## EducationNone of the above                                                  1.237789e-01
## EducationO levels/General Certificate of Secondary Education or equivalent  8.348850e-02
## EducationOther professional qualifications                                  9.114249e-02
## Income                                                                      9.293784e-03
## Average_time_outdoors                                                       1.010095e-02
## Summed_PA_min                                                               1.156526e-04
## Smoking                                                                    -2.038415e-02
## Disability                                                                 -4.765571e-03
## Deprivation_Index                                                           9.108382e-04
## Population_density                                                          1.805127e-02
## Natural_environment_300m_10pcnt:Sex                                         2.501959e-03

12) Crude models requested by Reviewer 2: using only 3 covariates: age, sex, and ethnic background

12.1) 1000m buffer

12.1.1) Cognitive Function

Association of natural environment with Trail-making Test B-A (not significant)

summary_confint(lm(Trails_B_A~Natural_environment_1000m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -132.492, -10.474, -2.668, 7.132, 179.467
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      28.67570    0.76184  37.640  < 2e-16 ***
## Natural_environment_1000m_10pcnt -0.06490    0.07599  -0.854    0.393    
## Age                               5.17089    0.23015  22.468  < 2e-16 ***
## Sex                               0.18824    0.34120   0.552    0.581    
## Race                             -5.83831    1.38576  -4.213 2.54e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.96 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.04362,    Adjusted R-squared:  0.04328 
## F-statistic: 129.3 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                       2.5 %      97.5 %
## (Intercept)                      27.1823730 30.16903460
## Natural_environment_1000m_10pcnt -0.2138423  0.08404903
## Age                               4.7197547  5.62201664
## Sex                              -0.4805831  0.85705819
## Race                             -8.5546500 -3.12197959

Association of natural environment with Symbol Digit Substitution (significant)

summary_confint(lm(Symbol.Digit~Natural_environment_1000m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -23.72, -2.555, 0.288, 2.88, 63.496
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      19.38579    0.18562 104.438  < 2e-16 ***
## Natural_environment_1000m_10pcnt  0.05549    0.01851   2.997  0.00273 ** 
## Age                              -2.67954    0.05608 -47.785  < 2e-16 ***
## Sex                              -0.09864    0.08313  -1.186  0.23547    
## Race                              2.11148    0.33764   6.254 4.15e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.377 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:   0.17,  Adjusted R-squared:  0.1697 
## F-statistic: 580.5 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %      97.5 %
## (Intercept)                      19.02194057 19.74963865
## Natural_environment_1000m_10pcnt  0.01920379  0.09178481
## Age                              -2.78946187 -2.56962636
## Sex                              -0.26159323  0.06432216
## Race                              1.44964479  2.77331126

Moderation by sex: Trail-making Test B-A (not significant)

summary_confint(lm(Trails_B_A~Natural_environment_1000m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -132.212, -10.472, -2.653, 7.146, 179.621
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          28.69886    0.76206  37.660  < 2e-16 ***
## Natural_environment_1000m_10pcnt     -0.06704    0.07601  -0.882    0.378    
## Sex                                  -0.68540    0.79752  -0.859    0.390    
## Age                                   5.17383    0.23016  22.480  < 2e-16 ***
## Race                                 -5.85576    1.38581  -4.226  2.4e-05 ***
## Natural_environment_1000m_10pcnt:Sex  0.18356    0.15146   1.212    0.226    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.96 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.04374,    Adjusted R-squared:  0.04332 
## F-statistic: 103.7 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                           2.5 %      97.5 %
## (Intercept)                          27.2050923 30.19263148
## Natural_environment_1000m_10pcnt     -0.2160263  0.08193975
## Sex                                  -2.2486882  0.87788102
## Age                                   4.7226870  5.62498069
## Race                                 -8.5721873 -3.13933599
## Natural_environment_1000m_10pcnt:Sex -0.1133233  0.48044324

Moderation by sex: Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Natural_environment_1000m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -23.732, -2.55, 0.297, 2.877, 63.479
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          19.38991    0.18568 104.426  < 2e-16 ***
## Natural_environment_1000m_10pcnt      0.05511    0.01852   2.976  0.00293 ** 
## Sex                                  -0.25422    0.19432  -1.308  0.19082    
## Age                                  -2.67902    0.05608 -47.772  < 2e-16 ***
## Race                                  2.10837    0.33766   6.244 4.42e-10 ***
## Natural_environment_1000m_10pcnt:Sex  0.03269    0.03690   0.886  0.37574    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.377 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:   0.17,  Adjusted R-squared:  0.1697 
## F-statistic: 464.6 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %      97.5 %
## (Intercept)                          19.02594679 19.75388066
## Natural_environment_1000m_10pcnt      0.01881130  0.09141272
## Sex                                  -0.63512298  0.12668648
## Age                                  -2.78894402 -2.56909415
## Race                                  1.44649576  2.77024624
## Natural_environment_1000m_10pcnt:Sex -0.03964824  0.10502694

12.1.2) Brain Volume

Association of natural environment with grey matter volume (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -173.494, -23.433, 0.295, 24.038, 171.318
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      788.9824     1.5175 519.907  < 2e-16 ***
## Natural_environment_1000m_10pcnt   0.4621     0.1514   3.053  0.00227 ** 
## Age                              -36.9131     0.4584 -80.518  < 2e-16 ***
## Sex                               25.0781     0.6797  36.898  < 2e-16 ***
## Race                               1.5234     2.7604   0.552  0.58104    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.78 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.4419, Adjusted R-squared:  0.4417 
## F-statistic:  2245 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %      97.5 %
## (Intercept)                      786.0077265 791.9570310
## Natural_environment_1000m_10pcnt   0.1653612   0.7587482
## Age                              -37.8117388 -36.0144710
## Sex                               23.7458085  26.4103337
## Race                              -3.8874288   6.9342224

Association of natural environment with white matter volume (significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.135, -26.227, -1.059, 24.419, 186.755
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      701.1136     1.6339 429.101  < 2e-16 ***
## Natural_environment_1000m_10pcnt   0.4830     0.1630   2.964  0.00304 ** 
## Age                              -16.8803     0.4936 -34.198  < 2e-16 ***
## Sex                               -9.0975     0.7318 -12.432  < 2e-16 ***
## Race                              -2.7943     2.9721  -0.940  0.34714    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.53 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.09885,    Adjusted R-squared:  0.09854 
## F-statistic:   311 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %      97.5 %
## (Intercept)                      697.9108281 704.3163371
## Natural_environment_1000m_10pcnt   0.1635794   0.8024685
## Age                              -17.8478861 -15.9128002
## Sex                              -10.5319533  -7.6631070
## Race                              -8.6200234   3.0314536

Association of natural environment with hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.602, -0.3112, 0.0258, 0.3417, 5.7042
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       4.9995238  0.0222687 224.509  < 2e-16 ***
## Natural_environment_1000m_10pcnt -0.0002966  0.0022213  -0.134  0.89376    
## Age                              -0.2155525  0.0067279 -32.039  < 2e-16 ***
## Sex                               0.2851969  0.0099757  28.589  < 2e-16 ***
## Race                             -0.1143976  0.0405054  -2.824  0.00475 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5251 on 11333 degrees of freedom
##   (110 observations deleted due to missingness)
## Multiple R-squared:  0.1629, Adjusted R-squared:  0.1626 
## F-statistic: 551.4 on 4 and 11333 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %       97.5 %
## (Intercept)                       4.95587331  5.043174363
## Natural_environment_1000m_10pcnt -0.00465073  0.004057436
## Age                              -0.22874030 -0.202364707
## Sex                               0.26564279  0.304751062
## Race                             -0.19379509 -0.035000048

Moderation by sex: Grey Matter (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -172.711, -23.35, 0.28, 24.146, 171.631
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          788.8994     1.5178 519.775  < 2e-16 ***
## Natural_environment_1000m_10pcnt       0.4697     0.1514   3.103  0.00192 ** 
## Sex                                   28.2082     1.5884  17.759  < 2e-16 ***
## Age                                  -36.9237     0.4584 -80.550  < 2e-16 ***
## Race                                   1.5859     2.7601   0.575  0.56558    
## Natural_environment_1000m_10pcnt:Sex  -0.6577     0.3017  -2.180  0.02926 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.78 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.4422, Adjusted R-squared:  0.4419 
## F-statistic:  1798 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %       97.5 %
## (Intercept)                          785.9243120 791.87450293
## Natural_environment_1000m_10pcnt       0.1730208   0.76647074
## Sex                                   25.0946239  31.32171667
## Age                                  -37.8222031 -36.02513230
## Race                                  -3.8243166   6.99612799
## Natural_environment_1000m_10pcnt:Sex  -1.2489558  -0.06636908

Moderation by sex: White Matter (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -148.379, -26.216, -1.109, 24.351, 186.277
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          701.0777     1.6344 428.939  < 2e-16 ***
## Natural_environment_1000m_10pcnt       0.4863     0.1630   2.983  0.00286 ** 
## Sex                                   -7.7450     1.7105  -4.528 6.02e-06 ***
## Age                                  -16.8849     0.4936 -34.205  < 2e-16 ***
## Race                                  -2.7673     2.9722  -0.931  0.35185    
## Natural_environment_1000m_10pcnt:Sex  -0.2842     0.3248  -0.875  0.38168    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.53 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.09891,    Adjusted R-squared:  0.09852 
## F-statistic: 248.9 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %      97.5 %
## (Intercept)                          697.8739351 704.2815249
## Natural_environment_1000m_10pcnt       0.1668127   0.8058820
## Sex                                  -11.0978760  -4.3920984
## Age                                  -17.8525145 -15.9173004
## Race                                  -8.5933874   3.0588389
## Natural_environment_1000m_10pcnt:Sex  -0.9209285   0.3525652

Moderation by sex: Average hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_1000m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_1000m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5993, -0.3114, 0.0257, 0.3422, 5.706
## 
## Coefficients:
##                                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                           4.9993145  0.0222766 224.420  < 2e-16 ***
## Natural_environment_1000m_10pcnt     -0.0002772  0.0022220  -0.125  0.90071    
## Sex                                   0.2930939  0.0233170  12.570  < 2e-16 ***
## Age                                  -0.2155790  0.0067285 -32.040  < 2e-16 ***
## Race                                 -0.1142398  0.0405091  -2.820  0.00481 ** 
## Natural_environment_1000m_10pcnt:Sex -0.0016591  0.0044278  -0.375  0.70788    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5251 on 11332 degrees of freedom
##   (110 observations deleted due to missingness)
## Multiple R-squared:  0.1629, Adjusted R-squared:  0.1626 
## F-statistic: 441.1 on 5 and 11332 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %       97.5 %
## (Intercept)                           4.95564863  5.042980450
## Natural_environment_1000m_10pcnt     -0.00463265  0.004078219
## Sex                                   0.24738860  0.338799290
## Age                                  -0.22876806 -0.202390004
## Race                                 -0.19364460 -0.034834950
## Natural_environment_1000m_10pcnt:Sex -0.01033836  0.007020098

12.2) 300m buffer

12.2.1) Cognitive Function

Association of natural environment with Trail-making Test B-A (not significant)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt + Age + 
##     Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -132.46, -10.463, -2.665, 7.129, 179.368
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     28.62023    0.72958  39.228  < 2e-16 ***
## Natural_environment_300m_10pcnt -0.06486    0.06941  -0.935    0.350    
## Age                              5.16935    0.23002  22.474  < 2e-16 ***
## Sex                              0.19217    0.34117   0.563    0.573    
## Race                            -5.85437    1.38445  -4.229 2.37e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.96 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.04363,    Adjusted R-squared:  0.0433 
## F-statistic: 129.3 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                      2.5 %      97.5 %
## (Intercept)                     27.1901268 30.05033370
## Natural_environment_300m_10pcnt -0.2009074  0.07118431
## Age                              4.7184742  5.62021925
## Sex                             -0.4765807  0.86092429
## Race                            -8.5681222 -3.14061340

Association of natural environment with Symbol Digit Substitution (significant)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -23.745, -2.55, 0.287, 2.87, 63.537
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     19.49718    0.17780 109.660  < 2e-16 ***
## Natural_environment_300m_10pcnt  0.03643    0.01691   2.154   0.0313 *  
## Age                             -2.67557    0.05605 -47.732  < 2e-16 ***
## Sex                             -0.10203    0.08314  -1.227   0.2198    
## Race                             2.14204    0.33739   6.349 2.25e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.378 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.1697, Adjusted R-squared:  0.1694 
## F-statistic: 579.2 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %      97.5 %
## (Intercept)                     19.148664365 19.84568971
## Natural_environment_300m_10pcnt  0.003277954  0.06958603
## Age                             -2.785446939 -2.56569390
## Sex                             -0.265000995  0.06094566
## Race                             1.480707758  2.80337824

Moderation by sex: Trail-making Test B-A (not significant)

summary_confint(lm(Trails_B_A~Natural_environment_300m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Trails_B_A ~ Natural_environment_300m_10pcnt * Sex + 
##     Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Trail making test (B-A; sec) 
## VALUES:
## -132.09, -10.482, -2.639, 7.188, 179.848
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         28.64134    0.72953  39.260  < 2e-16 ***
## Natural_environment_300m_10pcnt     -0.06796    0.06941  -0.979    0.328    
## Sex                                 -0.93410    0.62629  -1.491    0.136    
## Age                                  5.16688    0.22998  22.466  < 2e-16 ***
## Race                                -5.86877    1.38424  -4.240 2.26e-05 ***
## Natural_environment_300m_10pcnt:Sex  0.29706    0.13854   2.144    0.032 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.96 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.04402,    Adjusted R-squared:  0.0436 
## F-statistic: 104.4 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                           2.5 %      97.5 %
## (Intercept)                         27.21133379 30.07134743
## Natural_environment_300m_10pcnt     -0.20401730  0.06809034
## Sex                                 -2.16173183  0.29352479
## Age                                  4.71606979  5.61768310
## Race                                -8.58212137 -3.15540959
## Natural_environment_300m_10pcnt:Sex  0.02551082  0.56861801

Moderation by sex: Symbol Digit Substitution (not significant)

summary_confint(lm(Symbol.Digit~Natural_environment_300m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Symbol.Digit ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Symbol digit substitution test (correct matches) 
## VALUES:
## -23.746, -2.549, 0.289, 2.871, 63.536
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         19.497478   0.177821 109.647  < 2e-16 ***
## Natural_environment_300m_10pcnt      0.036388   0.016918   2.151   0.0315 *  
## Sex                                 -0.118091   0.152655  -0.774   0.4392    
## Age                                 -2.675606   0.056058 -47.730  < 2e-16 ***
## Race                                 2.141838   0.337405   6.348 2.26e-10 ***
## Natural_environment_300m_10pcnt:Sex  0.004237   0.033768   0.125   0.9002    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.378 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.1697, Adjusted R-squared:  0.1693 
## F-statistic: 463.4 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                           2.5 %      97.5 %
## (Intercept)                         19.14891858 19.84603767
## Natural_environment_300m_10pcnt      0.00322507  0.06955043
## Sex                                 -0.41732170  0.18113917
## Age                                 -2.78548832 -2.56572299
## Race                                 1.48046592  2.80320939
## Natural_environment_300m_10pcnt:Sex -0.06195341  0.07042722

12.2.2) Brain Volume

Association of natural environment with grey matter volume (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -173.681, -23.365, 0.329, 24.121, 171.555
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     789.4448     1.4532 543.229   <2e-16 ***
## Natural_environment_300m_10pcnt   0.4417     0.1382   3.195   0.0014 ** 
## Age                             -36.8993     0.4582 -80.537   <2e-16 ***
## Sex                              25.0500     0.6796  36.861   <2e-16 ***
## Race                              1.6555     2.7577   0.600   0.5483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.78 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.442,  Adjusted R-squared:  0.4418 
## F-statistic:  2245 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                      2.5 %      97.5 %
## (Intercept)                     786.596215 792.2934398
## Natural_environment_300m_10pcnt   0.170732   0.7127094
## Age                             -37.797433 -36.0012537
## Sex                              23.717947  26.3821135
## Race                             -3.750047   7.0609672

Association of natural environment with white matter volume (significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.611, -26.22, -1.111, 24.275, 187.756
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     701.8596     1.5649 448.503  < 2e-16 ***
## Natural_environment_300m_10pcnt   0.3836     0.1489   2.577  0.00998 ** 
## Age                             -16.8550     0.4934 -34.163  < 2e-16 ***
## Sex                              -9.1270     0.7318 -12.472  < 2e-16 ***
## Race                             -2.5871     2.9695  -0.871  0.38365    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.53 on 11339 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.09868,    Adjusted R-squared:  0.09837 
## F-statistic: 310.4 on 4 and 11339 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %      97.5 %
## (Intercept)                     698.79211050 704.9270298
## Natural_environment_300m_10pcnt   0.09182214   0.6754375
## Age                             -17.82213185 -15.8879595
## Sex                             -10.56137951  -7.6925363
## Race                             -8.40789077   3.2336898

Association of natural environment with hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt + Age + Sex + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt + 
##     Age + Sex + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5958, -0.3113, 0.026, 0.3411, 5.7052
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      5.007435   0.021324 234.822  < 2e-16 ***
## Natural_environment_300m_10pcnt -0.002727   0.002029  -1.344  0.17907    
## Age                             -0.215222   0.006723 -32.011  < 2e-16 ***
## Sex                              0.285213   0.009974  28.596  < 2e-16 ***
## Race                            -0.112320   0.040464  -2.776  0.00552 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.525 on 11333 degrees of freedom
##   (110 observations deleted due to missingness)
## Multiple R-squared:  0.163,  Adjusted R-squared:  0.1627 
## F-statistic: 551.9 on 4 and 11333 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                        2.5 %       97.5 %
## (Intercept)                      4.965635787  5.049234779
## Natural_environment_300m_10pcnt -0.006704136  0.001250909
## Age                             -0.228401530 -0.202043118
## Sex                              0.265662717  0.304764224
## Race                            -0.191635929 -0.033003260

Moderation by sex: Grey Matter (significant)

summary_confint(lm(Grey_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Grey_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Grey matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -173.005, -23.384, 0.248, 24.213, 172.056
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         789.3983     1.4531 543.258  < 2e-16 ***
## Natural_environment_300m_10pcnt       0.4486     0.1382   3.245  0.00118 ** 
## Sex                                  27.5317     1.2474  22.071  < 2e-16 ***
## Age                                 -36.8939     0.4581 -80.540  < 2e-16 ***
## Race                                  1.6872     2.7571   0.612  0.54059    
## Natural_environment_300m_10pcnt:Sex  -0.6546     0.2759  -2.372  0.01770 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35.77 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.4423, Adjusted R-squared:  0.442 
## F-statistic:  1798 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                           2.5 %      97.5 %
## (Intercept)                         786.5500212 792.2466025
## Natural_environment_300m_10pcnt       0.1775634   0.7195480
## Sex                                  25.0865292  29.9769146
## Age                                 -37.7918178 -35.9959825
## Race                                 -3.7172834   7.0916528
## Natural_environment_300m_10pcnt:Sex  -1.1954477  -0.1136856

Moderation by sex: White Matter (not significant)

summary_confint(lm(White_matter_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = White_matter_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: White matter volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -146.358, -26.165, -1.122, 24.372, 187.552
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         701.8407     1.5650 448.447  < 2e-16 ***
## Natural_environment_300m_10pcnt       0.3864     0.1489   2.595  0.00947 ** 
## Sex                                  -8.1216     1.3436  -6.045 1.54e-09 ***
## Age                                 -16.8528     0.4934 -34.158  < 2e-16 ***
## Race                                 -2.5742     2.9696  -0.867  0.38603    
## Natural_environment_300m_10pcnt:Sex  -0.2652     0.2972  -0.892  0.37227    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.53 on 11338 degrees of freedom
##   (104 observations deleted due to missingness)
## Multiple R-squared:  0.09875,    Adjusted R-squared:  0.09835 
## F-statistic: 248.5 on 5 and 11338 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %      97.5 %
## (Intercept)                         698.77295893 704.9084922
## Natural_environment_300m_10pcnt       0.09452514   0.6782725
## Sex                                 -10.75517034  -5.4879547
## Age                                 -17.81994753 -15.8857335
## Race                                 -8.39515922   3.2466630
## Natural_environment_300m_10pcnt:Sex  -0.84774013   0.3173775

Moderation by sex: Average hippocampal volume (not significant)

summary_confint(lm(Avg_Hippocampal_volume_adjusted_T2_cm3~Natural_environment_300m_10pcnt*Sex + Age + Race, CogsBrainCov.df2))
## [[1]]
## 
## Call:
## lm(formula = Avg_Hippocampal_volume_adjusted_T2_cm3 ~ Natural_environment_300m_10pcnt * 
##     Sex + Age + Race, data = CogsBrainCov.df2)
## 
## Residuals:
## LABEL: Average hippocampal volume at imaging study entry (adjusted for head size; mm^3) 
## VALUES:
## -3.5886, -0.31, 0.0254, 0.3396, 5.7073
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          5.007011   0.021325 234.792  < 2e-16 ***
## Natural_environment_300m_10pcnt     -0.002663   0.002030  -1.312  0.18946    
## Sex                                  0.307694   0.018313  16.802  < 2e-16 ***
## Age                                 -0.215170   0.006723 -32.004  < 2e-16 ***
## Race                                -0.112034   0.040462  -2.769  0.00563 ** 
## Natural_environment_300m_10pcnt:Sex -0.005929   0.004051  -1.464  0.14331    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.525 on 11332 degrees of freedom
##   (110 observations deleted due to missingness)
## Multiple R-squared:  0.1632, Adjusted R-squared:  0.1628 
## F-statistic:   442 on 5 and 11332 DF,  p-value: < 2.2e-16
## 
## 
## [[2]]
##                                            2.5 %       97.5 %
## (Intercept)                          4.965209461  5.048811976
## Natural_environment_300m_10pcnt     -0.006641505  0.001314948
## Sex                                  0.271797294  0.343590374
## Age                                 -0.228349212 -0.201991762
## Race                                -0.191346832 -0.032720307
## Natural_environment_300m_10pcnt:Sex -0.013869453  0.002011221